Solve 3k^2-2k-16=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

k_{1} = - 2, k_{2} = \frac{8}{3}

Alternative Form

k_{1} = - 2, k_{2} = 2. \dot{6}

Evaluate

3 k^{2} - 2 k - 16 = 0

Factor the expression

More Steps

Evaluate

3 k^{2} - 2 k - 16

Rewrite the expression

3 k^{2} + (- 8 + 6) k - 16

Calculate

3 k^{2} - 8 k + 6 k - 16

Rewrite the expression

k \times 3 k - k \times 8 + 2 \times 3 k - 2 \times 8

Factor out k from the expression

k (3 k - 8) + 2 \times 3 k - 2 \times 8

Factor out 2 from the expression

k (3 k - 8) + 2 (3 k - 8)

Factor out 3 k - 8 from the expression

(k + 2) (3 k - 8)

(k + 2) (3 k - 8) = 0

When the product of factors equals 0,at least one factor is 0

3 k - 8 = 0 k + 2 = 0

Solve the equation for k

More Steps

Evaluate

3 k - 8 = 0

Move the constant to the right-hand side and change its sign

3 k = 0 + 8

Removing 0 doesn't change the value,so remove it from the expression

3 k = 8

Divide both sides

\frac{3 k}{3} = \frac{8}{3}

Divide the numbers

k = \frac{8}{3}

k = \frac{8}{3} k + 2 = 0

Solve the equation for k

More Steps

Evaluate

k + 2 = 0

Move the constant to the right-hand side and change its sign

k = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

k = - 2

k = \frac{8}{3} k = - 2

Solution

k_{1} = - 2, k_{2} = \frac{8}{3}

Alternative Form

k_{1} = - 2, k_{2} = 2. \dot{6}

Show Solution