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Simplifying (2x + 1)(x + -2) = 52 Reorder the terms: (1 + 2x)(x + -2) = 52 Reorder the terms: (1 + 2x)(-2 + x) = 52 Multiply (1 + 2x) * (-2 + x) (1(-2 + x) + 2x * (-2 + x)) = 52 ((-2 * 1 + x * 1) + 2x * (-2 + x)) = 52 ((-2 + 1x) + 2x * (-2 + x)) = 52 (-2 + 1x + (-2 * 2x + x * 2x)) = 52 (-2 + 1x + (-4x + 2x2)) = 52 Combine like terms: 1x + -4x = -3x (-2 + -3x + 2x2) = 52 Solving -2 + -3x + 2x2 = 52 Solving for variable 'x'. Reorder the terms: -2 + -52 + -3x + 2x2 = 52 + -52 Combine like terms: -2 + -52 = -54 -54 + -3x + 2x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -54 + -3x + 2x2 = 0 Factor a trinomial. (-9 + -2x)(6 + -1x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-4.5, 6}
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