What are the solutions to the equation x^2+(x+6)^2=260 ?

The solutions to the equation x^2+(x+6)^2=260 are x=8,x=-14

Find the zeros of x^2+(x+6)^2=260

The zeros of x^2+(x+6)^2=260 are x=8,x=-14

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x^{2} + (x + 6)^{2} = 260

x = 8, x = - 14

Solution steps

x^{2} + (x + 6)^{2} = 260

Expand

x^{2} + (x + 6)^{2} : 2 x^{2} + 12 x + 36

2 x^{2} + 12 x + 36 = 260

Move

260

to the left side

2 x^{2} + 12 x - 224 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 2 ( - 224 )}{2 \cdot 2}

1 2^{2} - 4 \cdot 2 (- 224) = 44

x_{1, 2} = \frac{- 12 \pm 44}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 12 + 44}{2 \cdot 2}, x_{2} = \frac{- 12 - 44}{2 \cdot 2}

x = \frac{- 12 + 44}{2 \cdot 2} : 8

x = \frac{- 12 - 44}{2 \cdot 2} : - 14

The solutions to the quadratic equation are:

x = 8, x = - 14

x, y^{2} = 3 x^{2}

(x + 1) (x - 1) = 15

3 x^{2} + 27 x + 60 = 0

x^{2} - 10 x - 16 = 0

(x - 2) (x + 6) = 16

What are the solutions to the equation x^2+(x+6)^2=260 ?
The solutions to the equation x^2+(x+6)^2=260 are x=8,x=-14
Find the zeros of x^2+(x+6)^2=260
The zeros of x^2+(x+6)^2=260 are x=8,x=-14