What are the solutions to the equation 1/2 x^2+3x=-12 ?

The solutions to the equation 1/2 x^2+3x=-12 are x=-3+sqrt(15)i,x=-3-sqrt(15)i

Find the zeros of 1/2 x^2+3x=-12

The zeros of 1/2 x^2+3x=-12 are x=-3+sqrt(15)i,x=-3-sqrt(15)i

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\frac{1}{2} x^{2} + 3 x = - 12

x = - 3 + 15 i, x = - 3 - 15 i

Solution steps

\frac{1}{2} x^{2} + 3 x = - 12

Multiply both sides by

2

x^{2} + 6 x = - 24

Move

24

to the left side

x^{2} + 6 x + 24 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 1 \cdot 24}{2 \cdot 1}

Simplify

6^{2} - 4 \cdot 1 \cdot 24 : 215 i

x_{1, 2} = \frac{- 6 \pm 2 15 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 6 + 2 15 i}{2 \cdot 1}, x_{2} = \frac{- 6 - 2 15 i}{2 \cdot 1}

x = \frac{- 6 + 2 15 i}{2 \cdot 1} : - 3 + 15 i

x = \frac{- 6 - 2 15 i}{2 \cdot 1} : - 3 - 15 i

The solutions to the quadratic equation are:

x = - 3 + 15 i, x = - 3 - 15 i

x^{2} + 5 x - 1 = 0

- 3 x^{2} + 6 x - 1

\frac{1}{3} x^{2} + 3 x - 4 = - 4

x, x \cdot (x - y) + y \cdot (y - z) + z \cdot (z - x) = 1

n^{2} - 12 n = - 17

What are the solutions to the equation 1/2 x^2+3x=-12 ?
The solutions to the equation 1/2 x^2+3x=-12 are x=-3+sqrt(15)i,x=-3-sqrt(15)i
Find the zeros of 1/2 x^2+3x=-12
The zeros of 1/2 x^2+3x=-12 are x=-3+sqrt(15)i,x=-3-sqrt(15)i