Question

question 3 of 10
which choices are solutions to the following equation?
check all that apply.
$x^2 - 7x = -\frac{24}{4}$

a. $x = 12$
b. $x = 1$
c. $x = 6$
d. $x = 2$

Explanation:

Step1: Simplify the equation

First, simplify \(-\frac{24}{4}\) to \(-6\). So the equation becomes \(x^{2}-7x=-6\). Then, rewrite it in standard quadratic form \(ax^{2}+bx + c = 0\) by adding 6 to both sides: \(x^{2}-7x + 6=0\).

Step2: Factor the quadratic equation

Factor the quadratic expression \(x^{2}-7x + 6\). We need two numbers that multiply to 6 and add up to -7. The numbers are -1 and -6. So, \(x^{2}-7x + 6=(x - 1)(x - 6)=0\).

Step3: Solve for x

Set each factor equal to zero:

• For \(x - 1=0\), we get \(x = 1\).
• For \(x - 6=0\), we get \(x = 6\).

Answer:

B. \(x = 1\), C. \(x = 6\)