What are the solutions to the equation x^2+(4x+16)^2=(4x+17)^2 ?

The solutions to the equation x^2+(4x+16)^2=(4x+17)^2 are x=11,x=-3

Find the zeros of x^2+(4x+16)^2=(4x+17)^2

The zeros of x^2+(4x+16)^2=(4x+17)^2 are x=11,x=-3

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x^{2} + (4 x + 16)^{2} = (4 x + 17)^{2}

x = 11, x = - 3

Solution steps

x^{2} + (4 x + 16)^{2} = (4 x + 17)^{2}

Expand

x^{2} + (4 x + 16)^{2} : 17 x^{2} + 128 x + 256

Expand

(4 x + 17)^{2} : 16 x^{2} + 136 x + 289

17 x^{2} + 128 x + 256 = 16 x^{2} + 136 x + 289

Move

289

to the left side

17 x^{2} + 128 x - 33 = 16 x^{2} + 136 x

Move

136 x

to the left side

17 x^{2} - 8 x - 33 = 16 x^{2}

Move

16 x^{2}

to the left side

x^{2} - 8 x - 33 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot ( - 33 )}{2 \cdot 1}

(- 8)^{2} - 4 \cdot 1 \cdot (- 33) = 14

x_{1, 2} = \frac{- ( - 8 ) \pm 14}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 14}{2 \cdot 1}, x_{2} = \frac{- ( - 8 ) - 14}{2 \cdot 1}

x = \frac{- ( - 8 ) + 14}{2 \cdot 1} : 11

x = \frac{- ( - 8 ) - 14}{2 \cdot 1} : - 3

The solutions to the quadratic equation are:

x = 11, x = - 3

x^{2} + 2 x = 80

x^{2} + 2 x = 15

- 24 = - 3 x^{2} - 6 x

27 x^{2} + 5 = 48 x

2 x^{2} - 6 x - 18 = 0

What are the solutions to the equation x^2+(4x+16)^2=(4x+17)^2 ?
The solutions to the equation x^2+(4x+16)^2=(4x+17)^2 are x=11,x=-3
Find the zeros of x^2+(4x+16)^2=(4x+17)^2
The zeros of x^2+(4x+16)^2=(4x+17)^2 are x=11,x=-3