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Simplifying (2x + -7)(x + -5) = 2 Reorder the terms: (-7 + 2x)(x + -5) = 2 Reorder the terms: (-7 + 2x)(-5 + x) = 2 Multiply (-7 + 2x) * (-5 + x) (-7(-5 + x) + 2x * (-5 + x)) = 2 ((-5 * -7 + x * -7) + 2x * (-5 + x)) = 2 ((35 + -7x) + 2x * (-5 + x)) = 2 (35 + -7x + (-5 * 2x + x * 2x)) = 2 (35 + -7x + (-10x + 2x2)) = 2 Combine like terms: -7x + -10x = -17x (35 + -17x + 2x2) = 2 Solving 35 + -17x + 2x2 = 2 Solving for variable 'x'. Reorder the terms: 35 + -2 + -17x + 2x2 = 2 + -2 Combine like terms: 35 + -2 = 33 33 + -17x + 2x2 = 2 + -2 Combine like terms: 2 + -2 = 0 33 + -17x + 2x2 = 0 Factor a trinomial. (3 + -1x)(11 + -2x) = 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 '(11 + -2x)' equal to zero and attempt to solve: Simplifying 11 + -2x = 0 Solving 11 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2x = 0 + -11 -2x = 0 + -11 Combine like terms: 0 + -11 = -11 -2x = -11 Divide each side by '-2'. x = 5.5 Simplifying x = 5.5Solution
x = {3, 5.5}
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