Solve 8v^2-16v-8 - Socratic AI (ScanMath)

Evaluate

8 v^{2} - 16 v - 8

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

8 v^{2} - 16 v - 8 = 0

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

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

Simplify the expression

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

Simplify the expression

More Steps

v = \frac{16 \pm 512}{16}

Simplify the radical expression

More Steps

v = \frac{16 \pm 16 2}{16}

Separate the equation into 2 possible cases

v = \frac{16 + 16 2}{16} v = \frac{16 - 16 2}{16}

Simplify the expression

More Steps

v = 1 + 2 v = \frac{16 - 16 2}{16}

Simplify the expression

More Steps

v = 1 + 2 v = 1 - 2

Solution

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

Alternative Form

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

8v^2 16v 8