Question

solve by factoring.
$5x^2 + 12x + 4 = 0$
select the correct response:
$x = -2$
$x = -\frac{5}{2}$
$x = -2$
$x = -\frac{2}{5}$
$x = 2$
$x = \frac{2}{5}$
$x = 2$
$x = \frac{5}{2}$

Explanation:

Step1: Factor the quadratic equation

We need to factor \(5x^{2}+12x + 4 = 0\). We look for two numbers that multiply to \(5\times4=20\) and add up to \(12\). The numbers are \(10\) and \(2\).
So we rewrite the middle term:
\(5x^{2}+10x + 2x+4 = 0\)
Group the terms:
\((5x^{2}+10x)+(2x + 4)=0\)
Factor out the common factors from each group:
\(5x(x + 2)+2(x + 2)=0\)
Now factor out \((x + 2)\):
\((5x + 2)(x+2)=0\)

Step2: Solve for \(x\)

Set each factor equal to zero:

• For \(x + 2=0\), we get \(x=-2\)
• For \(5x+2 = 0\), we have \(5x=-2\), so \(x=-\frac{2}{5}\)

Answer:

\(x = - 2\)
\(x=-\frac{2}{5}\) (The option with these two solutions is the one with \(x=-2\) and \(x =-\frac{2}{5}\))