Question

question 3
1 pts
solve for x.
$5x^2 - 34x = -24$
select each correct answer.
-24
$\frac{4}{5}$
0
$\frac{34}{5}$
6

Explanation:

Step1: Rearrange the equation

First, we rewrite the quadratic equation \(5x^{2}-34x = - 24\) in standard form \(ax^{2}+bx + c=0\). Add 24 to both sides of the equation:
\(5x^{2}-34x + 24=0\)

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(5\times24 = 120\) and add up to \(- 34\). The numbers are \(-30\) and \(-4\).
Rewrite the middle term using these numbers:
\(5x^{2}-30x-4x + 24 = 0\)
Factor by grouping:
\(5x(x - 6)-4(x - 6)=0\)
\((5x - 4)(x - 6)=0\)

Step3: Solve for x

Set each factor equal to zero:

• For \(5x-4 = 0\), we have \(5x=4\), so \(x=\frac{4}{5}\)
• For \(x - 6=0\), we have \(x = 6\)

Answer:

\(\frac{4}{5}\), \(6\) (corresponding to the options: \(\frac{4}{5}\) and \(6\))