What are the solutions to the equation x^2+(x+1)^2=5^2 ?

The solutions to the equation x^2+(x+1)^2=5^2 are x=3,x=-4

Find the zeros of x^2+(x+1)^2=5^2

The zeros of x^2+(x+1)^2=5^2 are x=3,x=-4

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

x = 3, x = - 4

Solution steps

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

Expand

x^{2} + (x + 1)^{2} : 2 x^{2} + 2 x + 1

Expand

5^{2} : 25

2 x^{2} + 2 x + 1 = 25

Move

25

to the left side

2 x^{2} + 2 x - 24 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 2 ( - 24 )}{2 \cdot 2}

2^{2} - 4 \cdot 2 (- 24) = 14

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

Separate the solutions

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

x = \frac{- 2 + 14}{2 \cdot 2} : 3

x = \frac{- 2 - 14}{2 \cdot 2} : - 4

The solutions to the quadratic equation are:

x = 3, x = - 4

\frac{9 3}{3}

0.2 - \frac{4}{10} - 1.625

- 6.5 \leq \frac{7 x + 6}{2} \leq 20.5

0 = 3 x^{2} + 1

9 + 3 x > 12

What are the solutions to the equation x^2+(x+1)^2=5^2 ?
The solutions to the equation x^2+(x+1)^2=5^2 are x=3,x=-4
Find the zeros of x^2+(x+1)^2=5^2
The zeros of x^2+(x+1)^2=5^2 are x=3,x=-4