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Simplifying 2x(x + 4) = 42 Reorder the terms: 2x(4 + x) = 42 (4 * 2x + x * 2x) = 42 (8x + 2x2) = 42 Solving 8x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 8x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 4x + x2) = 0 Factor a trinomial. 2((-7 + -1x)(3 + -1x)) = 0 Ignore the factor 2.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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