What are the solutions to the equation (2x)^2+(2x+2)^2=452 ?

The solutions to the equation (2x)^2+(2x+2)^2=452 are x=7,x=-8

Find the zeros of (2x)^2+(2x+2)^2=452

The zeros of (2x)^2+(2x+2)^2=452 are x=7,x=-8

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(2 x)^{2} + (2 x + 2)^{2} = 452

x = 7, x = - 8

Solution steps

(2 x)^{2} + (2 x + 2)^{2} = 452

Expand

(2 x)^{2} + (2 x + 2)^{2} : 8 x^{2} + 8 x + 4

8 x^{2} + 8 x + 4 = 452

Move

452

to the left side

8 x^{2} + 8 x - 448 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 8 ( - 448 )}{2 \cdot 8}

8^{2} - 4 \cdot 8 (- 448) = 120

x_{1, 2} = \frac{- 8 \pm 120}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- 8 + 120}{2 \cdot 8}, x_{2} = \frac{- 8 - 120}{2 \cdot 8}

x = \frac{- 8 + 120}{2 \cdot 8} : 7

x = \frac{- 8 - 120}{2 \cdot 8} : - 8

The solutions to the quadratic equation are:

x = 7, x = - 8

4 - x^{2} = x - 2

2 k^{2} - 4 k = 96

4 x (x + 3) + (x + 2) (x - 2) = (2 x + 3)^{2} + x - 1

6 x^{2} = 12 x

2 x^{2} - 1 = 8 x

What are the solutions to the equation (2x)^2+(2x+2)^2=452 ?
The solutions to the equation (2x)^2+(2x+2)^2=452 are x=7,x=-8
Find the zeros of (2x)^2+(2x+2)^2=452
The zeros of (2x)^2+(2x+2)^2=452 are x=7,x=-8