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Simplifying 3x2 + -29x + 11 = 20x + -4x2 + -59 Reorder the terms: 11 + -29x + 3x2 = 20x + -4x2 + -59 Reorder the terms: 11 + -29x + 3x2 = -59 + 20x + -4x2 Solving 11 + -29x + 3x2 = -59 + 20x + -4x2 Solving for variable 'x'. Reorder the terms: 11 + 59 + -29x + -20x + 3x2 + 4x2 = -59 + 20x + -4x2 + 59 + -20x + 4x2 Combine like terms: 11 + 59 = 70 70 + -29x + -20x + 3x2 + 4x2 = -59 + 20x + -4x2 + 59 + -20x + 4x2 Combine like terms: -29x + -20x = -49x 70 + -49x + 3x2 + 4x2 = -59 + 20x + -4x2 + 59 + -20x + 4x2 Combine like terms: 3x2 + 4x2 = 7x2 70 + -49x + 7x2 = -59 + 20x + -4x2 + 59 + -20x + 4x2 Reorder the terms: 70 + -49x + 7x2 = -59 + 59 + 20x + -20x + -4x2 + 4x2 Combine like terms: -59 + 59 = 0 70 + -49x + 7x2 = 0 + 20x + -20x + -4x2 + 4x2 70 + -49x + 7x2 = 20x + -20x + -4x2 + 4x2 Combine like terms: 20x + -20x = 0 70 + -49x + 7x2 = 0 + -4x2 + 4x2 70 + -49x + 7x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 70 + -49x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(10 + -7x + x2) = 0 Factor a trinomial. 7((2 + -1x)(5 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {2, 5}
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