What are the solutions to the equation 2x^2+12x=x^2+8 ?

The solutions to the equation 2x^2+12x=x^2+8 are x=2(sqrt(11)-3),x=-2(3+sqrt(11))

Find the zeros of 2x^2+12x=x^2+8

The zeros of 2x^2+12x=x^2+8 are x=2(sqrt(11)-3),x=-2(3+sqrt(11))

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

x = 2 (11 - 3), x = - 2 (3 + 11)

Decimal Notation

x = 0.63324 \dots, x = - 12.63324 \dots

Solution steps

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

Move

8

to the left side

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

Move

x^{2}

to the left side

x^{2} + 12 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 1 \cdot ( - 8 )}{2 \cdot 1}

1 2^{2} - 4 \cdot 1 \cdot (- 8) = 411

x_{1, 2} = \frac{- 12 \pm 4 11}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 12 + 4 11}{2 \cdot 1}, x_{2} = \frac{- 12 - 4 11}{2 \cdot 1}

x = \frac{- 12 + 4 11}{2 \cdot 1} : 2 (11 - 3)

x = \frac{- 12 - 4 11}{2 \cdot 1} : - 2 (3 + 11)

The solutions to the quadratic equation are:

x = 2 (11 - 3), x = - 2 (3 + 11)

25 (3 - 5 x)^{2} - 4 = 12

y^{2} + 2 y - 2 = 0

x^{2} + x + 5

9 (x^{2} - 14) - 12 = - 17

20 x^{2} = - 25 x

What are the solutions to the equation 2x^2+12x=x^2+8 ?
The solutions to the equation 2x^2+12x=x^2+8 are x=2(sqrt(11)-3),x=-2(3+sqrt(11))
Find the zeros of 2x^2+12x=x^2+8
The zeros of 2x^2+12x=x^2+8 are x=2(sqrt(11)-3),x=-2(3+sqrt(11))