What are the solutions to the equation x^2+(x+14)^2=34^2 ?

The solutions to the equation x^2+(x+14)^2=34^2 are x=16,x=-30

Find the zeros of x^2+(x+14)^2=34^2

The zeros of x^2+(x+14)^2=34^2 are x=16,x=-30

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x^{2} + (x + 14)^{2} = 3 4^{2}

x = 16, x = - 30

Solution steps

x^{2} + (x + 14)^{2} = 3 4^{2}

Expand

x^{2} + (x + 14)^{2} : 2 x^{2} + 28 x + 196

Expand

3 4^{2} : 1156

2 x^{2} + 28 x + 196 = 1156

Move

1156

to the left side

2 x^{2} + 28 x - 960 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 28 \pm 2 8 ^{2} - 4 \cdot 2 ( - 960 )}{2 \cdot 2}

2 8^{2} - 4 \cdot 2 (- 960) = 92

x_{1, 2} = \frac{- 28 \pm 92}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 28 + 92}{2 \cdot 2}, x_{2} = \frac{- 28 - 92}{2 \cdot 2}

x = \frac{- 28 + 92}{2 \cdot 2} : 16

x = \frac{- 28 - 92}{2 \cdot 2} : - 30

The solutions to the quadratic equation are:

x = 16, x = - 30

X^{2} + 5 X - 14 = 0

x^{2} - \frac{2}{3} x

(x + 5)^{2} + 16 = 0

(x + 2) (x - 1) = 10

0 = 4 x^{2} - 4 x + 1

What are the solutions to the equation x^2+(x+14)^2=34^2 ?
The solutions to the equation x^2+(x+14)^2=34^2 are x=16,x=-30
Find the zeros of x^2+(x+14)^2=34^2
The zeros of x^2+(x+14)^2=34^2 are x=16,x=-30