Solve 3n^2 - 11n - 4 = 0

Question

Solve the quadratic equation

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

Alternative Form

n_{1} = - 0. \dot{3}, n_{2} = 4

Evaluate

3 n^{2} - 11 n - 4 = 0

Factor the expression

More Steps

Evaluate

3 n^{2} - 11 n - 4

Rewrite the expression

3 n^{2} + (1 - 12) n - 4

Calculate

3 n^{2} + n - 12 n - 4

Rewrite the expression

n \times 3 n + n - 4 \times 3 n - 4

Factor out n from the expression

n (3 n + 1) - 4 \times 3 n - 4

Factor out - 4 from the expression

n (3 n + 1) - 4 (3 n + 1)

Factor out 3 n + 1 from the expression

(n - 4) (3 n + 1)

(n - 4) (3 n + 1) = 0

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

n - 4 = 0 3 n + 1 = 0

Solve the equation for n

More Steps

Evaluate

n - 4 = 0

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

n = 0 + 4

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

n = 4

n = 4 3 n + 1 = 0

Solve the equation for n

More Steps

Evaluate

3 n + 1 = 0

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

3 n = 0 - 1

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

3 n = - 1

Divide both sides

\frac{3 n}{3} = \frac{- 1}{3}

Divide the numbers

n = \frac{- 1}{3}

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

n = - \frac{1}{3}

n = 4 n = - \frac{1}{3}

Solution

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

Alternative Form

n_{1} = - 0. \dot{3}, n_{2} = 4

Show Solution