Can You Solve This Math Problem:

[Kilgore Trout]

I was on a website reading an article about the planet Mars and saw this toss aside simple math problem sitting in a corner for some reason.
I've been tossing the problem around in my mind; but, it's been a long time since high school math and I forget how to solve algebra equations involving square roots.
So, here is the problem and if you know the answer can you explain the solution:


What is X:

SQRT (X+15) + SQRT (X) = 15


(Note: SQRT substitutes for math symbol for "the square root of" since my keyboard doesn't do that symbol)

 

[danmand]

49 .

 

[Kilgore Trout]

49 .

Yea, but I was looking at how the math breaks down so that if you got a more difficult square root X problem like

6 + 3x = SQRT(2x+12) + 2x

you'd be able to solve it

 

[dominator]

49 is the answer

I was on a website reading an article about the planet Mars and saw this toss aside simple math problem sitting in a corner for some reason.
I've been tossing the problem around in my mind; but, it's been a long time since high school math and I forget how to solve algebra equations involving square roots.
So, here is the problem and if you know the answer can you explain the solution:


What is X:

SQRT (X+15) + SQRT (X) = 15


(Note: SQRT substitutes for math symbol for "the square root of" since my keyboard doesn't do that symbol)

 

[waswarrior]

Here you go :

SQRT(x+15) + SQRT(x) = 15
(SQRT(x+15))² = (15 - SQRT(x))²
x+15 = 225 - 30SQRT(x) + x
30SQRT(x) = 210
(SQRT(x))² = 7²
x = 49

 

[Kilgore Trout]

Here you go :

SQRT(x+15) + SQRT(x) = 15
(SQRT(x+15))² = (15 - SQRT(x))²
x+15 = 225 - 30SQRT(x) + x
30SQRT(x) = 210
(SQRT(x))² = 7²
x = 49

Okay thanks.
Terb has at least one math wizard.

Key is to square both sides of the equation in the first step and then it becomes a more standard algebra equation

 

[danmand]

Simple solution:

Has to be square of a number, 4,9,16,25,36,Bingo

 

[Kilgore Trout]

Simple solution:

Has to be square of a number, 4,9,16,25,36,Bingo

That's a very smart observation that most people, myself included, don't clue in on right away.
Still it doesn't go into the guts of the machine, like waswarrior did, so that you can solve more difficult square root algebra problems.

 

[buttercup]

Yea, but I was looking at how the math breaks down so that if you got a more difficult square root X problem like
6 + 3x = SQRT(2x+12) + 2x
you'd be able to solve it

turning to the equation from Mars.

Very hard to deal directly with an equation that has SQRTs plus terms of other degrees in it. So your first task is to get rid of the SQRTs. In this case, you would subtract 2X from both sides:
6 + X =SQRT(2X + 12)
Now, square both sides:
36 + 2X +X2 = 2X +12
Now, subtract 2X from both sides:
36 + X2 = 12
or:
X2 = -24.

So, in your equation, X is the SQRT of a negative number
Meanwhile, back on the planet Mars . . .

 

[The "Bone" Ranger]

that was a very easy question

 

[danmand]

That's a very smart observation that most people, myself included, don't clue in on right away.
Still it doesn't go into the guts of the machine, like waswarrior did, so that you can solve more difficult square root algebra problems.

I am result oriented.

 

[frankcastle]

Okay thanks.
Terb has at least one math wizard.

Key is to square both sides of the equation in the first step and then it becomes a more standard algebra equation

Actually there are two keys..... first they rearranged the original equation and second when squaring both sides the right hand side of the equation is a binomial so when squaring a binomial you can follow the form.... (a +b)squared = a squared + a x b + b squared

 

[frankcastle]

Simple solution:

Has to be square of a number, 4,9,16,25,36,Bingo

Trial and error works but what if the question was set up so that the answer is not a "perfect square"

 

[Kilgore Trout]

turning to the equation from Mars.

Very hard to deal directly with an equation that has SQRTs plus terms of other degrees in it. So your first task is to get rid of the SQRTs. In this case, you would subtract 2X from both sides:
6 + X =SQRT(2X + 12)
Now, subtract 2X from both sides:Now, square both sides:
36 + 2X +X2 = 2X +12

36 + X2 = 12
or:
X2 = -24.

So, in your equation, X is the SQRT of a negative number
Meanwhile, back on the planet Mars . . .

I did some brief reading on square root algebra after reading the Mars article and actually the solution they give is different from yours.
When you write:

"Now, square both sides:
36 + 2X +X2 = 2X +12"

the correct solution they provide has the equation

36+12x+X^2 = 2x +12

X^2 +10X +24 =0
((X+6)(X+4)= 0

"we found two possible solutions : X = -6 and X = -4"

The full web solution is posted here:

https://www.khanacademy.org/math/al...ions/a/solving-square-root-equations-advanced

 

[buttercup]

I did some brief reading on square root algebra after reading the Mars article and actually the solution they give is different from yours.
When you write:

"Now, square both sides:
36 + 2X +X2 = 2X +12"

the correct solution they provide has the equation

36+12x+X^2 = 2x +12

X^2 +10X +24 =0
((X+6)(X+4)= 0

"we found two possible solutions : X = -6 and X = -4"

The full web solution is posted here:

https://www.khanacademy.org/math/al...ions/a/solving-square-root-equations-advanced

I think you're suggesting that (6 + X)^2 = 36 + 12X + X^2, and not the 36 + 2X + X^2 which is what I wrote.
You are correct, and yes the roots of the equation come out as you say.
I leave for Mars in the morning.

 

[danmand]

Trial and error works but what if the question was set up so that the answer is not a "perfect square"

Not trial and error. This problem obviously required whole numbers, no ifs about that. You are welcome to solve more general algebra cases.

Actually, I did not solve it by going through 4,9,16,25 ...

If you are a "numbers person", you just need 2 consecutive squares of whole numbers with a difference of 15, which is 7 and 8.

 

[waswarrior]

Well done Kilgore Trout.

 

[GPIDEAL]

Can you square both sides that are unequal?

I thought that what you did to one side you had to do to the other, as such (simplified demo):

SQRT(X) = 7

SQRT(X) x SQRT(X) = 7 x SQRT(X)

X = 7 x SQRT(X)

Now, substitute "SQRT(X)" with 7 from the first equation;


X = 7 x 7 = 49.

I guess I answered my own question (yes), but I had to prove it algebraically.

Next: The Theory of Relativity

 

[frankcastle]

Not trial and error. This problem obviously required whole numbers, no ifs about that. You are welcome to solve more general algebra cases.

Actually, I did not solve it by going through 4,9,16,25 ...

If you are a "numbers person", you just need 2 consecutive squares of whole numbers with a difference of 15, which is 7 and 8.

Maybe trial and error is not the right term but basically you were making an educated guess and checking.

 

[frankcastle]

I did some brief reading on square root algebra after reading the Mars article and actually the solution they give is different from yours.
When you write:

"Now, square both sides:
36 + 2X +X2 = 2X +12"

the correct solution they provide has the equation

36+12x+X^2 = 2x +12

X^2 +10X +24 =0
((X+6)(X+4)= 0

"we found two possible solutions : X = -6 and X = -4"

The full web solution is posted here:

https://www.khanacademy.org/math/al...ions/a/solving-square-root-equations-advanced

What you outlined there is solving a quadratic equation using factoring.

Not all quadratic equations can be factored..... the quadratic formula is needed for those situations