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What is the solution to the following equation?

[tex]\[ 4x^2 - 48x = -144 \][/tex]

A. [tex]\( x = -6 \)[/tex]

B. [tex]\( x = 6 \)[/tex]

C. [tex]\( x = -6, 36 \)[/tex]

D. [tex]\( x = 6, 36 \)[/tex]

Sagot :

GinnyAnswer
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]
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