Solve 5y^2 - 18y - 8 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - \frac{2}{5}, y_{2} = 4

Alternative Form

y_{1} = - 0.4, y_{2} = 4

Evaluate

5 y^{2} - 18 y - 8 = 0

Factor the expression

More Steps

Evaluate

5 y^{2} - 18 y - 8

Rewrite the expression

5 y^{2} + (2 - 20) y - 8

Calculate

5 y^{2} + 2 y - 20 y - 8

Rewrite the expression

y \times 5 y + y \times 2 - 4 \times 5 y - 4 \times 2

Factor out y from the expression

y (5 y + 2) - 4 \times 5 y - 4 \times 2

Factor out - 4 from the expression

y (5 y + 2) - 4 (5 y + 2)

Factor out 5 y + 2 from the expression

(y - 4) (5 y + 2)

(y - 4) (5 y + 2) = 0

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

y - 4 = 0 5 y + 2 = 0

Solve the equation for y

More Steps

Evaluate

y - 4 = 0

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

y = 0 + 4

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

y = 4

y = 4 5 y + 2 = 0

Solve the equation for y

More Steps

Evaluate

5 y + 2 = 0

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

5 y = 0 - 2

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

5 y = - 2

Divide both sides

\frac{5 y}{5} = \frac{- 2}{5}

Divide the numbers

y = \frac{- 2}{5}

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

y = - \frac{2}{5}

y = 4 y = - \frac{2}{5}

Solution

y_{1} = - \frac{2}{5}, y_{2} = 4

Alternative Form

y_{1} = - 0.4, y_{2} = 4

Show Solution