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Simplifying (x + -3)(x + -3) + (6 + -1x)(6 + -1x) = x * x Reorder the terms: (-3 + x)(x + -3) + (6 + -1x)(6 + -1x) = x * x Reorder the terms: (-3 + x)(-3 + x) + (6 + -1x)(6 + -1x) = x * x Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) + (6 + -1x)(6 + -1x) = x * x ((-3 * -3 + x * -3) + x(-3 + x)) + (6 + -1x)(6 + -1x) = x * x ((9 + -3x) + x(-3 + x)) + (6 + -1x)(6 + -1x) = x * x (9 + -3x + (-3 * x + x * x)) + (6 + -1x)(6 + -1x) = x * x (9 + -3x + (-3x + x2)) + (6 + -1x)(6 + -1x) = x * x Combine like terms: -3x + -3x = -6x (9 + -6x + x2) + (6 + -1x)(6 + -1x) = x * x Multiply (6 + -1x) * (6 + -1x) 9 + -6x + x2 + (6(6 + -1x) + -1x * (6 + -1x)) = x * x 9 + -6x + x2 + ((6 * 6 + -1x * 6) + -1x * (6 + -1x)) = x * x 9 + -6x + x2 + ((36 + -6x) + -1x * (6 + -1x)) = x * x 9 + -6x + x2 + (36 + -6x + (6 * -1x + -1x * -1x)) = x * x 9 + -6x + x2 + (36 + -6x + (-6x + 1x2)) = x * x Combine like terms: -6x + -6x = -12x 9 + -6x + x2 + (36 + -12x + 1x2) = x * x Reorder the terms: 9 + 36 + -6x + -12x + x2 + 1x2 = x * x Combine like terms: 9 + 36 = 45 45 + -6x + -12x + x2 + 1x2 = x * x Combine like terms: -6x + -12x = -18x 45 + -18x + x2 + 1x2 = x * x Combine like terms: x2 + 1x2 = 2x2 45 + -18x + 2x2 = x * x Multiply x * x 45 + -18x + 2x2 = x2 Solving 45 + -18x + 2x2 = x2 Solving for variable 'x'. Combine like terms: 2x2 + -1x2 = 1x2 45 + -18x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 45 + -18x + 1x2 = 0 Factor a trinomial. (3 + -1x)(15 + -1x) = 0Subproblem 1
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 = 3Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {3, 15}
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