Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward your grade.

solve the equation $6x^2 + x - 8 = 7$ by factoring. one of the solutions is provided. what is the other solution? give the answer as a fraction, not a decimal value. (1 point)

the solutions are $\frac{3}{2}$ and $\square$.

check answer remaining attempts: 3

Explanation:

Step1: Rearrange the equation

First, we need to rewrite the equation \(6x^{2}+x - 8=7\) in standard quadratic form \(ax^{2}+bx + c = 0\). Subtract 7 from both sides:
\(6x^{2}+x-8 - 7=0\)
\(6x^{2}+x - 15=0\)

Step2: Factor the quadratic

We need to factor \(6x^{2}+x - 15\). We look for two numbers that multiply to \(6\times(- 15)=-90\) and add up to 1. The numbers are 10 and - 9.
Rewrite the middle term:
\(6x^{2}+10x-9x - 15 = 0\)
Group the terms:
\((6x^{2}+10x)-(9x + 15)=0\)
Factor out the common factors from each group:
\(2x(3x + 5)-3(3x + 5)=0\)
Now, factor out \((3x + 5)\):
\((2x-3)(3x + 5)=0\)

Step3: Solve for x

Set each factor equal to zero:
\(2x-3 = 0\) or \(3x + 5=0\)
For \(2x-3 = 0\), we get \(x=\frac{3}{2}\) (which is the given solution).
For \(3x+5 = 0\), solve for x:
\(3x=-5\)
\(x =-\frac{5}{3}\)

Answer:

\(-\frac{5}{3}\)