Solve -6v^2-11v-4=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

v_{1} = - \frac{4}{3}, v_{2} = - \frac{1}{2}

Alternative Form

v_{1} = - 1. \dot{3}, v_{2} = - 0.5

Evaluate

- 6 v^{2} - 11 v - 4 = 0

Factor the expression

More Steps

Evaluate

- 6 v^{2} - 11 v - 4

Factor out - 1 from the expression

- (6 v^{2} + 11 v + 4)

Factor the expression

More Steps

Evaluate

6 v^{2} + 11 v + 4

Rewrite the expression

6 v^{2} + (8 + 3) v + 4

Calculate

6 v^{2} + 8 v + 3 v + 4

Rewrite the expression

2 v \times 3 v + 2 v \times 4 + 3 v + 4

Factor out 2 v from the expression

2 v (3 v + 4) + 3 v + 4

Factor out 3 v + 4 from the expression

(2 v + 1) (3 v + 4)

- (2 v + 1) (3 v + 4)

- (2 v + 1) (3 v + 4) = 0

Divide the terms

(2 v + 1) (3 v + 4) = 0

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

2 v + 1 = 0 3 v + 4 = 0

Solve the equation for v

More Steps

Evaluate

2 v + 1 = 0

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

2 v = 0 - 1

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

2 v = - 1

Divide both sides

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

Divide the numbers

v = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

v = - \frac{1}{2}

v = - \frac{1}{2} 3 v + 4 = 0

Solve the equation for v

More Steps

Evaluate

3 v + 4 = 0

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

3 v = 0 - 4

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

3 v = - 4

Divide both sides

\frac{3 v}{3} = \frac{- 4}{3}

Divide the numbers

v = \frac{- 4}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

v = - \frac{4}{3}

v = - \frac{1}{2} v = - \frac{4}{3}

Solution

v_{1} = - \frac{4}{3}, v_{2} = - \frac{1}{2}

Alternative Form

v_{1} = - 1. \dot{3}, v_{2} = - 0.5

Show Solution