What are the solutions to the equation x^2+(x+20)^2=(2x-20)^2 ?

The solutions to the equation x^2+(x+20)^2=(2x-20)^2 are x=0,x=60

Find the zeros of x^2+(x+20)^2=(2x-20)^2

The zeros of x^2+(x+20)^2=(2x-20)^2 are x=0,x=60

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x^{2} + (x + 20)^{2} = (2 x - 20)^{2}

x = 0, x = 60

Solution steps

x^{2} + (x + 20)^{2} = (2 x - 20)^{2}

Expand

x^{2} + (x + 20)^{2} : 2 x^{2} + 40 x + 400

Expand

(2 x - 20)^{2} : 4 x^{2} - 80 x + 400

2 x^{2} + 40 x + 400 = 4 x^{2} - 80 x + 400

Move

400

to the left side

2 x^{2} + 40 x = 4 x^{2} - 80 x

Move

80 x

to the left side

2 x^{2} + 120 x = 4 x^{2}

Move

4 x^{2}

to the left side

- 2 x^{2} + 120 x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 120 \pm 12 0 ^{2} - 4 ( - 2 ) \cdot 0}{2 ( - 2 )}

12 0^{2} - 4 (- 2) \cdot 0 = 120

x_{1, 2} = \frac{- 120 \pm 120}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 120 + 120}{2 ( - 2 )}, x_{2} = \frac{- 120 - 120}{2 ( - 2 )}

x = \frac{- 120 + 120}{2 ( - 2 )} : 0

x = \frac{- 120 - 120}{2 ( - 2 )} : 60

The solutions to the quadratic equation are:

x = 0, x = 60

x, 2 x^{2} - 3 y^{2} = 2 x y - 6

5 x^{2} = - 5 x + 1

\frac{1}{10} x (10 - x) - 2 = 0

3 n^{2} + 10 n = - 12 - 8 n^{2} + 10 n

m^{2} + 24 m

What are the solutions to the equation x^2+(x+20)^2=(2x-20)^2 ?
The solutions to the equation x^2+(x+20)^2=(2x-20)^2 are x=0,x=60
Find the zeros of x^2+(x+20)^2=(2x-20)^2
The zeros of x^2+(x+20)^2=(2x-20)^2 are x=0,x=60