Solve 72s^2-351s-45=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

s_{1} = - \frac{1}{8}, s_{2} = 5

Alternative Form

s_{1} = - 0.125, s_{2} = 5

Evaluate

72 s^{2} - 351 s - 45 = 0

Factor the expression

More Steps

Evaluate

72 s^{2} - 351 s - 45

Rewrite the expression

9 \times 8 s^{2} - 9 \times 39 s - 9 \times 5

Factor out 9 from the expression

9 (8 s^{2} - 39 s - 5)

Factor the expression

More Steps

Evaluate

8 s^{2} - 39 s - 5

Rewrite the expression

8 s^{2} + (1 - 40) s - 5

Calculate

8 s^{2} + s - 40 s - 5

Rewrite the expression

s \times 8 s + s - 5 \times 8 s - 5

Factor out s from the expression

s (8 s + 1) - 5 \times 8 s - 5

Factor out - 5 from the expression

s (8 s + 1) - 5 (8 s + 1)

Factor out 8 s + 1 from the expression

(s - 5) (8 s + 1)

9 (s - 5) (8 s + 1)

9 (s - 5) (8 s + 1) = 0

Divide the terms

(s - 5) (8 s + 1) = 0

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

s - 5 = 0 8 s + 1 = 0

Solve the equation for s

More Steps

Evaluate

s - 5 = 0

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

s = 0 + 5

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

s = 5

s = 5 8 s + 1 = 0

Solve the equation for s

More Steps

Evaluate

8 s + 1 = 0

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

8 s = 0 - 1

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

8 s = - 1

Divide both sides

\frac{8 s}{8} = \frac{- 1}{8}

Divide the numbers

s = \frac{- 1}{8}

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

s = - \frac{1}{8}

s = 5 s = - \frac{1}{8}

Solution

s_{1} = - \frac{1}{8}, s_{2} = 5

Alternative Form

s_{1} = - 0.125, s_{2} = 5

Show Solution