To solve the quadratic equation [tex]\(4x^2 - 48x = -144\)[/tex], follow these steps:
1. Move all terms to one side to set the equation to zero:
[tex]\[
4x^2 - 48x + 144 = 0
\][/tex]
2. Simplify the equation by dividing all terms by the greatest common divisor, which is 4:
[tex]\[
x^2 - 12x + 36 = 0
\][/tex]
3. Recognize that this is a quadratic equation of the form [tex]\(ax^2 + bx + c = 0\)[/tex]. Here, [tex]\(a = 1\)[/tex], [tex]\(b = -12\)[/tex], and [tex]\(c = 36\)[/tex].
4. Factor the quadratic equation:
[tex]\[
x^2 - 12x + 36 = (x - 6)(x - 6) = (x - 6)^2 = 0
\][/tex]
5. Set each factor equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[
(x - 6)^2 = 0 \implies x - 6 = 0 \implies x = 6
\][/tex]
There is only one solution to the equation, which is:
[tex]\[
x = 6
\][/tex]
So, the correct answer is:
B. [tex]\(x = 6\)[/tex]
