Question

1. $5x^2 - 16x - 16 = 0$

Explanation:

Step1: Factor the quadratic equation

We need to factor \(5x^2 - 16x - 16 = 0\). We look for two numbers that multiply to \(5\times(-16)=-80\) and add up to \(-16\). The numbers are \(-20\) and \(4\).
So we rewrite the middle term: \(5x^2 - 20x + 4x - 16 = 0\)
Group the terms: \((5x^2 - 20x)+(4x - 16)=0\)
Factor out the common factors: \(5x(x - 4)+4(x - 4)=0\)
Then we get \((5x + 4)(x - 4)=0\)

Step2: Solve for x

Set each factor equal to zero:

• \(5x + 4 = 0\) gives \(5x=-4\), so \(x = -\frac{4}{5}\)
• \(x - 4 = 0\) gives \(x = 4\)

Answer:

\(x = 4\) or \(x = -\frac{4}{5}\)