What are the solutions to the equation (x-2)^2+(x+8)^2=10^2 ?

The solutions to the equation (x-2)^2+(x+8)^2=10^2 are x=2,x=-8

Find the zeros of (x-2)^2+(x+8)^2=10^2

The zeros of (x-2)^2+(x+8)^2=10^2 are x=2,x=-8

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(x - 2)^{2} + (x + 8)^{2} = 1 0^{2}

x = 2, x = - 8

Solution steps

(x - 2)^{2} + (x + 8)^{2} = 1 0^{2}

Expand

(x - 2)^{2} + (x + 8)^{2} : 2 x^{2} + 12 x + 68

Expand

1 0^{2} : 100

2 x^{2} + 12 x + 68 = 100

Move

100

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 2 ( - 32 )}{2 \cdot 2}

1 2^{2} - 4 \cdot 2 (- 32) = 20

x_{1, 2} = \frac{- 12 \pm 20}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 12 + 20}{2 \cdot 2}, x_{2} = \frac{- 12 - 20}{2 \cdot 2}

x = \frac{- 12 + 20}{2 \cdot 2} : 2

x = \frac{- 12 - 20}{2 \cdot 2} : - 8

The solutions to the quadratic equation are:

x = 2, x = - 8

3 x^{2} + 3 x = 25 x - x^{2}

5 x^{2} + 5 = - 15

2 x^{2} - 6 = 3 x

5 x^{2} + x = - 5

7 x + 120 = x^{2}

What are the solutions to the equation (x-2)^2+(x+8)^2=10^2 ?
The solutions to the equation (x-2)^2+(x+8)^2=10^2 are x=2,x=-8
Find the zeros of (x-2)^2+(x+8)^2=10^2
The zeros of (x-2)^2+(x+8)^2=10^2 are x=2,x=-8