Solve (2s^2)-9s=5

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

s_{1} = - 0.5, s_{2} = 5

Evaluate

2 s^{2} - 9 s = 5

Move the expression to the left side

2 s^{2} - 9 s - 5 = 0

Factor the expression

More Steps

Evaluate

2 s^{2} - 9 s - 5

Rewrite the expression

2 s^{2} + (1 - 10) s - 5

Calculate

2 s^{2} + s - 10 s - 5

Rewrite the expression

s \times 2 s + s - 5 \times 2 s - 5

Factor out s from the expression

s (2 s + 1) - 5 \times 2 s - 5

Factor out - 5 from the expression

s (2 s + 1) - 5 (2 s + 1)

Factor out 2 s + 1 from the expression

(s - 5) (2 s + 1)

(s - 5) (2 s + 1) = 0

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

s - 5 = 0 2 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 2 s + 1 = 0

Solve the equation for s

More Steps

Evaluate

2 s + 1 = 0

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

2 s = 0 - 1

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

2 s = - 1

Divide both sides

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

Divide the numbers

s = \frac{- 1}{2}

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

s = - \frac{1}{2}

s = 5 s = - \frac{1}{2}

Solution

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

Alternative Form

s_{1} = - 0.5, s_{2} = 5

Show Solution