What are the solutions to the equation X^2+(X+7)^2=13^2 ?

The solutions to the equation X^2+(X+7)^2=13^2 are X=5,X=-12

Find the zeros of X^2+(X+7)^2=13^2

The zeros of X^2+(X+7)^2=13^2 are X=5,X=-12

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X^{2} + (X + 7)^{2} = 1 3^{2}

X = 5, X = - 12

Solution steps

X^{2} + (X + 7)^{2} = 1 3^{2}

Expand

X^{2} + (X + 7)^{2} : 2 X^{2} + 14 X + 49

Expand

1 3^{2} : 169

2 X^{2} + 14 X + 49 = 169

Move

169

to the left side

2 X^{2} + 14 X - 120 = 0

Solve with the quadratic formula

X_{1, 2} = \frac{- 14 \pm 1 4 ^{2} - 4 \cdot 2 ( - 120 )}{2 \cdot 2}

1 4^{2} - 4 \cdot 2 (- 120) = 34

X_{1, 2} = \frac{- 14 \pm 34}{2 \cdot 2}

Separate the solutions

X_{1} = \frac{- 14 + 34}{2 \cdot 2}, X_{2} = \frac{- 14 - 34}{2 \cdot 2}

X = \frac{- 14 + 34}{2 \cdot 2} : 5

X = \frac{- 14 - 34}{2 \cdot 2} : - 12

The solutions to the quadratic equation are:

X = 5, X = - 12

3 x^{2} - 10 x + 13 = 0

3 x^{1} + x^{2} = 10

x^{2} + 3 x - 28 = 0

1 2^{2} = x^{2} + 8^{2}

x, x^{2} + y^{2} + 10 x - 4 y + 33 = 0

What are the solutions to the equation X^2+(X+7)^2=13^2 ?
The solutions to the equation X^2+(X+7)^2=13^2 are X=5,X=-12
Find the zeros of X^2+(X+7)^2=13^2
The zeros of X^2+(X+7)^2=13^2 are X=5,X=-12