What are the solutions to the equation (2x+3)^2=117-x^2 ?

The solutions to the equation (2x+3)^2=117-x^2 are x= 18/5 ,x=-6

Find the zeros of (2x+3)^2=117-x^2

The zeros of (2x+3)^2=117-x^2 are x= 18/5 ,x=-6

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(2 x + 3)^{2} = 117 - x^{2}

x = \frac{18}{5}, x = - 6

Decimal Notation

x = 3.6, x = - 6

Solution steps

(2 x + 3)^{2} = 117 - x^{2}

Expand

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

4 x^{2} + 12 x + 9 = 117 - x^{2}

Move

x^{2}

to the left side

5 x^{2} + 12 x + 9 = 117

Move

117

to the left side

5 x^{2} + 12 x - 108 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 5 ( - 108 )}{2 \cdot 5}

1 2^{2} - 4 \cdot 5 (- 108) = 48

x_{1, 2} = \frac{- 12 \pm 48}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- 12 + 48}{2 \cdot 5}, x_{2} = \frac{- 12 - 48}{2 \cdot 5}

x = \frac{- 12 + 48}{2 \cdot 5} : \frac{18}{5}

x = \frac{- 12 - 48}{2 \cdot 5} : - 6

The solutions to the quadratic equation are:

x = \frac{18}{5}, x = - 6

2 x^{2} + (x - 15)^{2} = 4 x + 185

x^{2} + 24 x + 140 = 0

15 x^{2} + 12 = - 8 x

x^{2} - 3 x = 12 - 3 (x - 2)

x^{2} + 120 x + 10000 = 0

What are the solutions to the equation (2x+3)^2=117-x^2 ?
The solutions to the equation (2x+3)^2=117-x^2 are x= 18/5 ,x=-6
Find the zeros of (2x+3)^2=117-x^2
The zeros of (2x+3)^2=117-x^2 are x= 18/5 ,x=-6