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Simplifying 3(x + -3)(x + -3) + x2 = x(x + 62) + -50x Reorder the terms: 3(-3 + x)(x + -3) + x2 = x(x + 62) + -50x Reorder the terms: 3(-3 + x)(-3 + x) + x2 = x(x + 62) + -50x Multiply (-3 + x) * (-3 + x) 3(-3(-3 + x) + x(-3 + x)) + x2 = x(x + 62) + -50x 3((-3 * -3 + x * -3) + x(-3 + x)) + x2 = x(x + 62) + -50x 3((9 + -3x) + x(-3 + x)) + x2 = x(x + 62) + -50x 3(9 + -3x + (-3 * x + x * x)) + x2 = x(x + 62) + -50x 3(9 + -3x + (-3x + x2)) + x2 = x(x + 62) + -50x Combine like terms: -3x + -3x = -6x 3(9 + -6x + x2) + x2 = x(x + 62) + -50x (9 * 3 + -6x * 3 + x2 * 3) + x2 = x(x + 62) + -50x (27 + -18x + 3x2) + x2 = x(x + 62) + -50x Combine like terms: 3x2 + x2 = 4x2 27 + -18x + 4x2 = x(x + 62) + -50x Reorder the terms: 27 + -18x + 4x2 = x(62 + x) + -50x 27 + -18x + 4x2 = (62 * x + x * x) + -50x 27 + -18x + 4x2 = (62x + x2) + -50x Reorder the terms: 27 + -18x + 4x2 = 62x + -50x + x2 Combine like terms: 62x + -50x = 12x 27 + -18x + 4x2 = 12x + x2 Solving 27 + -18x + 4x2 = 12x + x2 Solving for variable 'x'. Reorder the terms: 27 + -18x + -12x + 4x2 + -1x2 = 12x + x2 + -12x + -1x2 Combine like terms: -18x + -12x = -30x 27 + -30x + 4x2 + -1x2 = 12x + x2 + -12x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 27 + -30x + 3x2 = 12x + x2 + -12x + -1x2 Reorder the terms: 27 + -30x + 3x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 27 + -30x + 3x2 = 0 + x2 + -1x2 27 + -30x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 27 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -10x + x2) = 0 Factor a trinomial. 3((1 + -1x)(9 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {1, 9}
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