Solve 5y^2 - 28y -220 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - \frac{22}{5}, y_{2} = 10

Alternative Form

y_{1} = - 4.4, y_{2} = 10

Evaluate

5 y^{2} - 28 y - 220 = 0

Factor the expression

More Steps

Evaluate

5 y^{2} - 28 y - 220

Rewrite the expression

5 y^{2} + (22 - 50) y - 220

Calculate

5 y^{2} + 22 y - 50 y - 220

Rewrite the expression

y \times 5 y + y \times 22 - 10 \times 5 y - 10 \times 22

Factor out y from the expression

y (5 y + 22) - 10 \times 5 y - 10 \times 22

Factor out - 10 from the expression

y (5 y + 22) - 10 (5 y + 22)

Factor out 5 y + 22 from the expression

(y - 10) (5 y + 22)

(y - 10) (5 y + 22) = 0

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

y - 10 = 0 5 y + 22 = 0

Solve the equation for y

More Steps

Evaluate

y - 10 = 0

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

y = 0 + 10

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

y = 10

y = 10 5 y + 22 = 0

Solve the equation for y

More Steps

Evaluate

5 y + 22 = 0

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

5 y = 0 - 22

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

5 y = - 22

Divide both sides

\frac{5 y}{5} = \frac{- 22}{5}

Divide the numbers

y = \frac{- 22}{5}

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

y = - \frac{22}{5}

y = 10 y = - \frac{22}{5}

Solution

y_{1} = - \frac{22}{5}, y_{2} = 10

Alternative Form

y_{1} = - 4.4, y_{2} = 10

Show Solution