Solve 4x^2-9x-9=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{3}{4}, x_{2} = 3

Alternative Form

x_{1} = - 0.75, x_{2} = 3

Evaluate

4 x^{2} - 9 x - 9 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 9 x - 9

Rewrite the expression

4 x^{2} + (3 - 12) x - 9

Calculate

4 x^{2} + 3 x - 12 x - 9

Rewrite the expression

x \times 4 x + x \times 3 - 3 \times 4 x - 3 \times 3

Factor out x from the expression

x (4 x + 3) - 3 \times 4 x - 3 \times 3

Factor out - 3 from the expression

x (4 x + 3) - 3 (4 x + 3)

Factor out 4 x + 3 from the expression

(x - 3) (4 x + 3)

(x - 3) (4 x + 3) = 0

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

x - 3 = 0 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 3 = 0

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

4 x = 0 - 3

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

4 x = - 3

Divide both sides

\frac{4 x}{4} = \frac{- 3}{4}

Divide the numbers

x = \frac{- 3}{4}

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

x = - \frac{3}{4}

x = 3 x = - \frac{3}{4}

Solution

x_{1} = - \frac{3}{4}, x_{2} = 3

Alternative Form

x_{1} = - 0.75, x_{2} = 3

Show Solution