Solve -16x^2-12x-108

Question

Factor the expression

- 4 (4 x^{2} + 3 x + 27)

Show Solution

x_{1} = - \frac{3}{8} - \frac{3 47}{8} i, x_{2} = - \frac{3}{8} + \frac{3 47}{8} i

Alternative Form

x_{1} \approx - 0.375 - 2.57087 i, x_{2} \approx - 0.375 + 2.57087 i

Evaluate

- 16 x^{2} - 12 x - 108

To find the roots of the expression,set the expression equal to 0

- 16 x^{2} - 12 x - 108 = 0

Multiply both sides

16 x^{2} + 12 x + 108 = 0

Substitute a= 16,b= 12 and c= 108 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 12 \pm 1 2 ^{2} - 4 \times 16 \times 108}{2 \times 16}

Simplify the expression

x = \frac{- 12 \pm 1 2 ^{2} - 4 \times 16 \times 108}{32}

Simplify the expression

More Steps

x = \frac{- 12 \pm - 6768}{32}

Simplify the radical expression

More Steps

x = \frac{- 12 \pm 12 47 \times i}{32}

Separate the equation into 2 possible cases

x = \frac{- 12 + 12 47 \times i}{32} x = \frac{- 12 - 12 47 \times i}{32}

Simplify the expression

More Steps

x = - \frac{3}{8} + \frac{3 47}{8} i x = \frac{- 12 - 12 47 \times i}{32}

Simplify the expression

More Steps

x = - \frac{3}{8} + \frac{3 47}{8} i x = - \frac{3}{8} - \frac{3 47}{8} i

Solution

x_{1} = - \frac{3}{8} - \frac{3 47}{8} i, x_{2} = - \frac{3}{8} + \frac{3 47}{8} i

Alternative Form

x_{1} \approx - 0.375 - 2.57087 i, x_{2} \approx - 0.375 + 2.57087 i

Show Solution