Solve 16 x^2 - 32x -16 =0

Evaluate

16 x^{2} - 32 x - 16 = 0

Substitute a= 16,b= - 32 and c= - 16 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{32 \pm 2048}{32}

Simplify the radical expression

More Steps

x = \frac{32 \pm 32 2}{32}

Separate the equation into 2 possible cases

x = \frac{32 + 32 2}{32} x = \frac{32 - 32 2}{32}

Simplify the expression

More Steps

x = 1 + 2 x = \frac{32 - 32 2}{32}

Simplify the expression

More Steps

x = 1 + 2 x = 1 - 2

Solution

x_{1} = 1 - 2, x_{2} = 1 + 2

Alternative Form

x_{1} \approx - 0.414214, x_{2} \approx 2.414214

Solve the quadratic equation