What are the solutions to the equation (x+3)^2+x^2=269 ?

The solutions to the equation (x+3)^2+x^2=269 are x=10,x=-13

Find the zeros of (x+3)^2+x^2=269

The zeros of (x+3)^2+x^2=269 are x=10,x=-13

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(x + 3)^{2} + x^{2} = 269

x = 10, x = - 13

Solution steps

(x + 3)^{2} + x^{2} = 269

Expand

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

2 x^{2} + 6 x + 9 = 269

Move

269

to the left side

2 x^{2} + 6 x - 260 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 2 ( - 260 )}{2 \cdot 2}

6^{2} - 4 \cdot 2 (- 260) = 46

x_{1, 2} = \frac{- 6 \pm 46}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 6 + 46}{2 \cdot 2}, x_{2} = \frac{- 6 - 46}{2 \cdot 2}

x = \frac{- 6 + 46}{2 \cdot 2} : 10

x = \frac{- 6 - 46}{2 \cdot 2} : - 13

The solutions to the quadratic equation are:

x = 10, x = - 13

Y^{2} + 4 Y = 0

(x - 2)^{2} = (2 x - 3)^{2} - 1

3 x^{2} - 18 x - 21 = 0

8 0^{2} + 6 0^{2} = x^{2}

x, x^{2} + 6 x = - 5

What are the solutions to the equation (x+3)^2+x^2=269 ?
The solutions to the equation (x+3)^2+x^2=269 are x=10,x=-13
Find the zeros of (x+3)^2+x^2=269
The zeros of (x+3)^2+x^2=269 are x=10,x=-13