Solve 36k^2 - 32k - 77 = 0

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

k_{1} = \frac{8 - 757}{18}, k_{2} = \frac{8 + 757}{18}

Alternative Form

k_{1} \approx - 1.084091, k_{2} \approx 1.97298

Evaluate

36 k^{2} - 32 k - 77 = 0

Substitute a= 36,b= - 32 and c= - 77 into the quadratic formula k = \frac{- b \pm b ^{2} - 4 a c}{2 a}

k = \frac{32 \pm ( - 32 ) ^{2} - 4 \times 36 ( - 77 )}{2 \times 36}

Simplify the expression

k = \frac{32 \pm ( - 32 ) ^{2} - 4 \times 36 ( - 77 )}{72}

Simplify the expression

More Steps

k = \frac{32 \pm 12112}{72}

Simplify the radical expression

More Steps

k = \frac{32 \pm 4 757}{72}

Separate the equation into 2 possible cases

k = \frac{32 + 4 757}{72} k = \frac{32 - 4 757}{72}

Simplify the expression

More Steps

k = \frac{8 + 757}{18} k = \frac{32 - 4 757}{72}

Simplify the expression

More Steps

k = \frac{8 + 757}{18} k = \frac{8 - 757}{18}

Solution

k_{1} = \frac{8 - 757}{18}, k_{2} = \frac{8 + 757}{18}

Alternative Form

k_{1} \approx - 1.084091, k_{2} \approx 1.97298

Show Solution