Solve -8x = 16x^(2) - 27

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{1 + 2 7}{4}, x_{2} = \frac{- 1 + 2 7}{4}

Alternative Form

x_{1} \approx - 1.572876, x_{2} \approx 1.072876

Evaluate

- 8 x = 16 x^{2} - 27

Swap the sides

16 x^{2} - 27 = - 8 x

Move the expression to the left side

16 x^{2} - 27 + 8 x = 0

Rewrite in standard form

16 x^{2} + 8 x - 27 = 0

Substitute a= 16,b= 8 and c= - 27 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 8 \pm 8 ^{2} - 4 \times 16 ( - 27 )}{2 \times 16}

Simplify the expression

x = \frac{- 8 \pm 8 ^{2} - 4 \times 16 ( - 27 )}{32}

Simplify the expression

More Steps

x = \frac{- 8 \pm 1792}{32}

Simplify the radical expression

More Steps

x = \frac{- 8 \pm 16 7}{32}

Separate the equation into 2 possible cases

x = \frac{- 8 + 16 7}{32} x = \frac{- 8 - 16 7}{32}

Simplify the expression

More Steps

x = \frac{- 1 + 2 7}{4} x = \frac{- 8 - 16 7}{32}

Simplify the expression

More Steps

x = \frac{- 1 + 2 7}{4} x = - \frac{1 + 2 7}{4}

Solution

x_{1} = - \frac{1 + 2 7}{4}, x_{2} = \frac{- 1 + 2 7}{4}

Alternative Form

x_{1} \approx - 1.572876, x_{2} \approx 1.072876

Show Solution