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Simplifying 4x2 + 12x + 9 = 72 + x2 Reorder the terms: 9 + 12x + 4x2 = 72 + x2 Solving 9 + 12x + 4x2 = 72 + x2 Solving for variable 'x'. Reorder the terms: 9 + -72 + 12x + 4x2 + -1x2 = 72 + x2 + -72 + -1x2 Combine like terms: 9 + -72 = -63 -63 + 12x + 4x2 + -1x2 = 72 + x2 + -72 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -63 + 12x + 3x2 = 72 + x2 + -72 + -1x2 Reorder the terms: -63 + 12x + 3x2 = 72 + -72 + x2 + -1x2 Combine like terms: 72 + -72 = 0 -63 + 12x + 3x2 = 0 + x2 + -1x2 -63 + 12x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -63 + 12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 4x + x2) = 0 Factor a trinomial. 3((-7 + -1x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-7, 3}
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