Question

question 1 of 10
find the solutions to the equation below.
check all that apply.
6x² + 7x - 5 = 0
a. x = -5/3
b. x = -2
c. x = 1/3
d. x = 5
e. x = 1/2
f. x = -1/3

Explanation:

Step1: Factor the quadratic equation

For the quadratic equation \(6x^{2}+7x - 5=0\), we need to find two numbers \(m\) and \(n\) such that \(m\times n=6\times(- 5)=-30\) and \(m + n=7\). The numbers are \(10\) and \(-3\). Then we rewrite the middle - term: \(6x^{2}+10x-3x - 5 = 0\). Group the terms: \((6x^{2}+10x)-(3x + 5)=0\). Factor out the greatest common factor from each group: \(2x(3x + 5)-1(3x + 5)=0\). Then \((2x - 1)(3x+5)=0\).

Step2: Set each factor equal to zero

If \(2x - 1=0\), then \(2x=1\), and \(x=\frac{1}{2}\). If \(3x + 5=0\), then \(3x=-5\), and \(x =-\frac{5}{3}\).

Answer:

A. \(x =-\frac{5}{3}\)
E. \(x=\frac{1}{2}\)