Solve z^2 - 14z - 11 = 0

Evaluate

z^{2} - 14 z - 11 = 0

Substitute a= 1,b= - 14 and c= - 11 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{14 \pm ( - 14 ) ^{2} - 4 ( - 11 )}{2}

Simplify the expression

More Steps

z = \frac{14 \pm 240}{2}

Simplify the radical expression

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z = \frac{14 \pm 4 15}{2}

Separate the equation into 2 possible cases

z = \frac{14 + 4 15}{2} z = \frac{14 - 4 15}{2}

Simplify the expression

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z = 7 + 215 z = \frac{14 - 4 15}{2}

Simplify the expression

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z = 7 + 215 z = 7 - 215

Solution

z_{1} = 7 - 215, z_{2} = 7 + 215

Alternative Form

z_{1} \approx - 0.745967, z_{2} \approx 14.745967

Solve the quadratic equation