What are the solutions to the equation (x-5)^2+x^2=(x+5)^2 ?

The solutions to the equation (x-5)^2+x^2=(x+5)^2 are x=20,x=0

Find the zeros of (x-5)^2+x^2=(x+5)^2

The zeros of (x-5)^2+x^2=(x+5)^2 are x=20,x=0

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(x - 5)^{2} + x^{2} = (x + 5)^{2}

x = 20, x = 0

Solution steps

(x - 5)^{2} + x^{2} = (x + 5)^{2}

Expand

(x - 5)^{2} + x^{2} : 2 x^{2} - 10 x + 25

Expand

(x + 5)^{2} : x^{2} + 10 x + 25

2 x^{2} - 10 x + 25 = x^{2} + 10 x + 25

Move

25

to the left side

2 x^{2} - 10 x = x^{2} + 10 x

Move

10 x

to the left side

2 x^{2} - 20 x = x^{2}

Move

x^{2}

to the left side

x^{2} - 20 x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

(- 20)^{2} - 4 \cdot 1 \cdot 0 = 20

x_{1, 2} = \frac{- ( - 20 ) \pm 20}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 20}{2 \cdot 1}, x_{2} = \frac{- ( - 20 ) - 20}{2 \cdot 1}

x = \frac{- ( - 20 ) + 20}{2 \cdot 1} : 20

x = \frac{- ( - 20 ) - 20}{2 \cdot 1} : 0

The solutions to the quadratic equation are:

x = 20, x = 0

9 x^{2} + 12 x - 32 = 0

(x + 6)^{2} + 12 (x + 6) + 27 = 0

\frac{1}{8} + \frac{3}{4}

12 5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

b^{2} - b - 2 = 0

What are the solutions to the equation (x-5)^2+x^2=(x+5)^2 ?
The solutions to the equation (x-5)^2+x^2=(x+5)^2 are x=20,x=0
Find the zeros of (x-5)^2+x^2=(x+5)^2
The zeros of (x-5)^2+x^2=(x+5)^2 are x=20,x=0