Certainly! Let's solve the quadratic equation [tex]\(4x^2 + 24x = 4\)[/tex] by completing the square step by step.
First, let's rewrite the equation in standard quadratic form:
[tex]\[ 4x^2 + 24x - 4 = 0 \][/tex]
Step 1: Divide the entire equation by 4 to simplify it:
[tex]\[ x^2 + 6x - 1 = 0 \][/tex]
Step 2: Move the constant term to the right side:
[tex]\[ x^2 + 6x = 1 \][/tex]
Step 3: To complete the square, we take half of the coefficient of [tex]\(x\)[/tex] (which is 6), square it, and add it to both sides of the equation:
[tex]\[ \left(\frac{6}{2}\right)^2 = 3^2 = 9 \][/tex]
[tex]\[ x^2 + 6x + 9 = 1 + 9 \][/tex]
[tex]\[ (x + 3)^2 = 10 \][/tex]
Step 4: To solve for [tex]\(x\)[/tex], we take the square root of both sides:
[tex]\[ x + 3 = \pm \sqrt{10} \][/tex]
Step 5: Solve for [tex]\(x\)[/tex] by isolating it:
[tex]\[ x = -3 \pm \sqrt{10} \][/tex]
Thus, the solutions to the quadratic equation [tex]\(4x^2 + 24x = 4\)[/tex] are:
[tex]\[ \boxed{-3 \pm \sqrt{10}} \][/tex]
By matching these solutions with the given choices, we identify the correct answer:
[tex]\[ A. x = -3 \pm \sqrt{10} \][/tex]
