Solve 8y^2-4y-4=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

y_{1} = - 0.5, y_{2} = 1

Evaluate

8 y^{2} - 4 y - 4 = 0

Factor the expression

More Steps

Evaluate

8 y^{2} - 4 y - 4

Rewrite the expression

4 \times 2 y^{2} - 4 y - 4

Factor out 4 from the expression

4 (2 y^{2} - y - 1)

Factor the expression

More Steps

Evaluate

2 y^{2} - y - 1

Rewrite the expression

2 y^{2} + (1 - 2) y - 1

Calculate

2 y^{2} + y - 2 y - 1

Rewrite the expression

y \times 2 y + y - 2 y - 1

Factor out y from the expression

y (2 y + 1) - 2 y - 1

Factor out - 1 from the expression

y (2 y + 1) - (2 y + 1)

Factor out 2 y + 1 from the expression

(y - 1) (2 y + 1)

4 (y - 1) (2 y + 1)

4 (y - 1) (2 y + 1) = 0

Divide the terms

(y - 1) (2 y + 1) = 0

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

y - 1 = 0 2 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

y - 1 = 0

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

y = 0 + 1

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

y = 1

y = 1 2 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

2 y + 1 = 0

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

2 y = 0 - 1

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

2 y = - 1

Divide both sides

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

Divide the numbers

y = \frac{- 1}{2}

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

y = - \frac{1}{2}

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

Solution

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

Alternative Form

y_{1} = - 0.5, y_{2} = 1

Show Solution