What are the solutions to the equation x^2+(x+3)^2=15^2 ?

The solutions to the equation x^2+(x+3)^2=15^2 are x=9,x=-12

Find the zeros of x^2+(x+3)^2=15^2

The zeros of x^2+(x+3)^2=15^2 are x=9,x=-12

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x^{2} + (x + 3)^{2} = 1 5^{2}

x = 9, x = - 12

Solution steps

x^{2} + (x + 3)^{2} = 1 5^{2}

Expand

x^{2} + (x + 3)^{2} : 2 x^{2} + 6 x + 9

Expand

1 5^{2} : 225

2 x^{2} + 6 x + 9 = 225

Move

225

to the left side

2 x^{2} + 6 x - 216 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 2 ( - 216 )}{2 \cdot 2}

6^{2} - 4 \cdot 2 (- 216) = 42

x_{1, 2} = \frac{- 6 \pm 42}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 6 + 42}{2 \cdot 2}, x_{2} = \frac{- 6 - 42}{2 \cdot 2}

x = \frac{- 6 + 42}{2 \cdot 2} : 9

x = \frac{- 6 - 42}{2 \cdot 2} : - 12

The solutions to the quadratic equation are:

x = 9, x = - 12

(6 + 2 x) (10 + 2 x) - 60 = 36

3 a x^{2} + 2 b x + c = 0

x^{2} + 12 x + 10 = 0

2 x^{2} - 4 x - 16 = 0

x^{2} + 18 x + 81 = 121

What are the solutions to the equation x^2+(x+3)^2=15^2 ?
The solutions to the equation x^2+(x+3)^2=15^2 are x=9,x=-12
Find the zeros of x^2+(x+3)^2=15^2
The zeros of x^2+(x+3)^2=15^2 are x=9,x=-12