Solve -4x^2-23x-15=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 5, x_{2} = - \frac{3}{4}

Alternative Form

x_{1} = - 5, x_{2} = - 0.75

Evaluate

- 4 x^{2} - 23 x - 15 = 0

Factor the expression

More Steps

Evaluate

- 4 x^{2} - 23 x - 15

Factor out - 1 from the expression

- (4 x^{2} + 23 x + 15)

Factor the expression

More Steps

Evaluate

4 x^{2} + 23 x + 15

Rewrite the expression

4 x^{2} + (3 + 20) x + 15

Calculate

4 x^{2} + 3 x + 20 x + 15

Rewrite the expression

x \times 4 x + x \times 3 + 5 \times 4 x + 5 \times 3

Factor out x from the expression

x (4 x + 3) + 5 \times 4 x + 5 \times 3

Factor out 5 from the expression

x (4 x + 3) + 5 (4 x + 3)

Factor out 4 x + 3 from the expression

(x + 5) (4 x + 3)

- (x + 5) (4 x + 3)

- (x + 5) (4 x + 3) = 0

Divide the terms

(x + 5) (4 x + 3) = 0

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

4 x + 3 = 0 x + 5 = 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 = - \frac{3}{4} x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x + 5 = 0

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

x = 0 - 5

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

x = - 5

x = - \frac{3}{4} x = - 5

Solution

x_{1} = - 5, x_{2} = - \frac{3}{4}

Alternative Form

x_{1} = - 5, x_{2} = - 0.75

Show Solution