What are the solutions to the equation (x+5)^2+x^2=18^2 ?

The solutions to the equation (x+5)^2+x^2=18^2 are x=(-5+sqrt(623))/2 ,x=-(5+sqrt(623))/2

Find the zeros of (x+5)^2+x^2=18^2

The zeros of (x+5)^2+x^2=18^2 are x=(-5+sqrt(623))/2 ,x=-(5+sqrt(623))/2

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(x + 5)^{2} + x^{2} = 1 8^{2}

x = \frac{- 5 + 623}{2}, x = - \frac{5 + 623}{2}

Decimal Notation

x = 9.97998 \dots, x = - 14.97998 \dots

Solution steps

(x + 5)^{2} + x^{2} = 1 8^{2}

Expand

(x + 5)^{2} + x^{2} : 2 x^{2} + 10 x + 25

Expand

1 8^{2} : 324

2 x^{2} + 10 x + 25 = 324

Move

324

to the left side

2 x^{2} + 10 x - 299 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 \cdot 2 ( - 299 )}{2 \cdot 2}

1 0^{2} - 4 \cdot 2 (- 299) = 2623

x_{1, 2} = \frac{- 10 \pm 2 623}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 10 + 2 623}{2 \cdot 2}, x_{2} = \frac{- 10 - 2 623}{2 \cdot 2}

x = \frac{- 10 + 2 623}{2 \cdot 2} : \frac{- 5 + 623}{2}

x = \frac{- 10 - 2 623}{2 \cdot 2} : - \frac{5 + 623}{2}

The solutions to the quadratic equation are:

x = \frac{- 5 + 623}{2}, x = - \frac{5 + 623}{2}

62 - 62 x = (8 x + 2) (x - 1)

(x + 4)^{2} = x^{2} + (x + 2)^{2}

5 - 2 x - x^{2} = 0

x^{2} = \frac{5}{3}

3 x^{2} + 67 = 5 x^{2} + 17

What are the solutions to the equation (x+5)^2+x^2=18^2 ?
The solutions to the equation (x+5)^2+x^2=18^2 are x=(-5+sqrt(623))/2 ,x=-(5+sqrt(623))/2
Find the zeros of (x+5)^2+x^2=18^2
The zeros of (x+5)^2+x^2=18^2 are x=(-5+sqrt(623))/2 ,x=-(5+sqrt(623))/2