Question

Use factoring to solve the equation. Use a graphing calculator to check your solution if you wish. $$-\frac{4}{5} x^{2}-\frac{4}{5} x-\frac{1}{5}=0$$

Short answer

The solution to the equation is \(x = -\frac{1}{2}\).

Step-by-step solution

Write original equation

Let's start with the given equation: \(-\frac{4}{5} x^{2}-\frac{4}{5} x-\frac{1}{5}=0\)

Multiply the equation

In order to simplify, it is useful to get rid of fractions. Multiply both sides by -5: \(4x^2 + 4x + 1 = 0\).

Apply the perfect square rule

After looking at the simplified equation, one can realize that this quadratic equation can be factored as a perfect square. Apply the perfect square rule: \( (2x+1)^2 = 0\).

Solve for x

The equation \((2x+1)^2 =0\) implies that \(2x+1=0\) which is solved by isolating x: \(x = -\frac{1}{2}\)