Solve 2y ^ 2 + 9y + 10 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

y_{1} = - 2.5, y_{2} = - 2

Evaluate

2 y^{2} + 9 y + 10 = 0

Factor the expression

More Steps

Evaluate

2 y^{2} + 9 y + 10

Rewrite the expression

2 y^{2} + (5 + 4) y + 10

Calculate

2 y^{2} + 5 y + 4 y + 10

Rewrite the expression

y \times 2 y + y \times 5 + 2 \times 2 y + 2 \times 5

Factor out y from the expression

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

Factor out 2 from the expression

y (2 y + 5) + 2 (2 y + 5)

Factor out 2 y + 5 from the expression

(y + 2) (2 y + 5)

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

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

y + 2 = 0 2 y + 5 = 0

Solve the equation for y

More Steps

Evaluate

y + 2 = 0

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

y = 0 - 2

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

y = - 2

y = - 2 2 y + 5 = 0

Solve the equation for y

More Steps

Evaluate

2 y + 5 = 0

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

2 y = 0 - 5

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

2 y = - 5

Divide both sides

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

Divide the numbers

y = \frac{- 5}{2}

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

y = - \frac{5}{2}

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

Solution

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

Alternative Form

y_{1} = - 2.5, y_{2} = - 2

Show Solution