What are the solutions to the equation x^2+(x+17)^2=25^2 ?

The solutions to the equation x^2+(x+17)^2=25^2 are x=7,x=-24

Find the zeros of x^2+(x+17)^2=25^2

The zeros of x^2+(x+17)^2=25^2 are x=7,x=-24

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x^{2} + (x + 17)^{2} = 2 5^{2}

x = 7, x = - 24

Solution steps

x^{2} + (x + 17)^{2} = 2 5^{2}

Expand

x^{2} + (x + 17)^{2} : 2 x^{2} + 34 x + 289

Expand

2 5^{2} : 625

2 x^{2} + 34 x + 289 = 625

Move

625

to the left side

2 x^{2} + 34 x - 336 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 34 \pm 3 4 ^{2} - 4 \cdot 2 ( - 336 )}{2 \cdot 2}

3 4^{2} - 4 \cdot 2 (- 336) = 62

x_{1, 2} = \frac{- 34 \pm 62}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 34 + 62}{2 \cdot 2}, x_{2} = \frac{- 34 - 62}{2 \cdot 2}

x = \frac{- 34 + 62}{2 \cdot 2} : 7

x = \frac{- 34 - 62}{2 \cdot 2} : - 24

The solutions to the quadratic equation are:

x = 7, x = - 24

2 x^{2} + 11 x + 14

5 - 10

2^{\frac{1}{2}} \cdot 2^{\frac{3}{5}}

2 (3 x + 2 y)^{2} - 12 x - 8 y

- ∣ b + 4 ∣ - 1 = 10

What are the solutions to the equation x^2+(x+17)^2=25^2 ?
The solutions to the equation x^2+(x+17)^2=25^2 are x=7,x=-24
Find the zeros of x^2+(x+17)^2=25^2
The zeros of x^2+(x+17)^2=25^2 are x=7,x=-24