Solve 14n^2 - 29n - 108 =0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - \frac{27}{14}, n_{2} = 4

Alternative Form

n_{1} = - 1.9 \dot{2} 8571 \dot{4}, n_{2} = 4

Evaluate

14 n^{2} - 29 n - 108 = 0

Factor the expression

More Steps

Evaluate

14 n^{2} - 29 n - 108

Rewrite the expression

14 n^{2} + (27 - 56) n - 108

Calculate

14 n^{2} + 27 n - 56 n - 108

Rewrite the expression

n \times 14 n + n \times 27 - 4 \times 14 n - 4 \times 27

Factor out n from the expression

n (14 n + 27) - 4 \times 14 n - 4 \times 27

Factor out - 4 from the expression

n (14 n + 27) - 4 (14 n + 27)

Factor out 14 n + 27 from the expression

(n - 4) (14 n + 27)

(n - 4) (14 n + 27) = 0

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

n - 4 = 0 14 n + 27 = 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 14 n + 27 = 0

Solve the equation for n

More Steps

Evaluate

14 n + 27 = 0

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

14 n = 0 - 27

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

14 n = - 27

Divide both sides

\frac{14 n}{14} = \frac{- 27}{14}

Divide the numbers

n = \frac{- 27}{14}

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

n = - \frac{27}{14}

n = 4 n = - \frac{27}{14}

Solution

n_{1} = - \frac{27}{14}, n_{2} = 4

Alternative Form

n_{1} = - 1.9 \dot{2} 8571 \dot{4}, n_{2} = 4

Show Solution