How do you find x if the square root of x plus the square root of (x minus 20) equals 10

√x + √(x - 20) = 10

Squaring both sides:

x + 2√(x² - 20x) + x - 20 = 100

2x + 2√(x² - 20x) = 120

√(x² - 20x) = 60 - x

Squaring again:

x² - 20x = 3600 - 120x + x²

100x = 3600

x = 36

Hey Captain Matticus, it seems like we both made the same mistake.. We forgot to square the 10 on the other side.. I edited my question because of that.

√x + √(x-20) = 10

Square both sides
x + 2√(x(x-20)) + x - 20 = 100

Now rearrange to isolate the remaining radical
√(x(x-20)) = 60 - x

Square both sides again
x(x-20) = 3600 - 120x + x^2
x^2 - 20x = 3600 - 120x + x^2
100x = 3600
x = 36

Check: √36 + √(36-20) = √36 + √16 = 6 + 4 = 10

sqrt(x) + sqrt(x-20) = 10

Square both sides:
x + 2*sqrt(x)sqrt(x-20) + x -20=100
2( x + sqrt(x)sqrt(x-20) ) = 120
x+ sqrt(x)sqrt(x-20) = 60
sqrt(x^2-20x) = 60 -x <- remember sqrt(a)sqrt(b) = sqrt(ab)

Square both sides again:
x^2 -20x = 3600 - 120x + x^2
100x = 3600
x = 36

Check answer: sqrt(36) + sqrt(x-20) = 6+4 = 10
Correct!

I think :

sqrt(x-20) = 10 - sqrt (x) squaring both sides yields

x-20 = 100 -20 sqrt (x) +x combining and segregating

20 sqrt(x) = 120

sqrt (x) = 6 squaring both sides yields

x =36

√(x) + √(x - 20) = 10
√(x - 20)^2 = [10 - √(x)]^2
x - 20 = x-20√(x)+100
x - x - 100 - 20 = - 20√(x)
(- 120)^2 = [- 20 √(x)]^2
14,400 = 400x
x = 36 answer//

sqrt(x) + sqrt(x - 20) = 10

Square both sides of the equation

x + 2 * sqrt(x) * sqrt(x - 20) + x - 20 = 10
2 * sqrt(x) * sqrt(x - 20) = 10 + 20 - 2x
2 * sqrt(x) * sqrt(x - 20) = 30 - 2x
sqrt(x) * sqrt(x - 20) = 15 - x

Square both sides again

x * (x - 20) = 225 - 30x + x^2
x^2 - 20x = 225 - 30x + x^2
-20x = 225 - 30x
30x - 20x = 225
10x = 225
x = 22.5

√x + √(x - 20) = 10

let x = x
let x - 20 = y

√x + √y = 10
(√x + √y)^2 = 10^2
(√x + √y)(√x + √y) = 100
x + √xy + √xy + y = 100
2√xy = 100 - x - y
4xy = (100 - x - y)^2
4xy = (100 - x - y)(100 - x - y)
4xy = 10000 - 100x - 100y - 100x + x^2 + xy - 100y + xy + y^2
4xy = 10000 - 200x - 200y + x^2 + 2xy + y^2
0 = 10000 - 200x - 200y + x^2 - 2xy + y^2

now you can sub in for y

0 = 10000 - 200x - 200(x - 20) + x^2 - 2x(x - 20) + (x - 20)^2
0 = 10000 - 200x - 200x + 4000 + x^2 - 2x^2 + 40x + x^2 - 40x + 400
0 = 14400 - 400x
400x = 14400
x = 36