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Simplifying 9x2 + -1(7x + -2)(x + 3) = -12x + 1 Reorder the terms: 9x2 + -1(-2 + 7x)(x + 3) = -12x + 1 Reorder the terms: 9x2 + -1(-2 + 7x)(3 + x) = -12x + 1 Multiply (-2 + 7x) * (3 + x) 9x2 + -1(-2(3 + x) + 7x * (3 + x)) = -12x + 1 9x2 + -1((3 * -2 + x * -2) + 7x * (3 + x)) = -12x + 1 9x2 + -1((-6 + -2x) + 7x * (3 + x)) = -12x + 1 9x2 + -1(-6 + -2x + (3 * 7x + x * 7x)) = -12x + 1 9x2 + -1(-6 + -2x + (21x + 7x2)) = -12x + 1 Combine like terms: -2x + 21x = 19x 9x2 + -1(-6 + 19x + 7x2) = -12x + 1 9x2 + (-6 * -1 + 19x * -1 + 7x2 * -1) = -12x + 1 9x2 + (6 + -19x + -7x2) = -12x + 1 Reorder the terms: 6 + -19x + 9x2 + -7x2 = -12x + 1 Combine like terms: 9x2 + -7x2 = 2x2 6 + -19x + 2x2 = -12x + 1 Reorder the terms: 6 + -19x + 2x2 = 1 + -12x Solving 6 + -19x + 2x2 = 1 + -12x Solving for variable 'x'. Reorder the terms: 6 + -1 + -19x + 12x + 2x2 = 1 + -12x + -1 + 12x Combine like terms: 6 + -1 = 5 5 + -19x + 12x + 2x2 = 1 + -12x + -1 + 12x Combine like terms: -19x + 12x = -7x 5 + -7x + 2x2 = 1 + -12x + -1 + 12x Reorder the terms: 5 + -7x + 2x2 = 1 + -1 + -12x + 12x Combine like terms: 1 + -1 = 0 5 + -7x + 2x2 = 0 + -12x + 12x 5 + -7x + 2x2 = -12x + 12x Combine like terms: -12x + 12x = 0 5 + -7x + 2x2 = 0 Factor a trinomial. (1 + -1x)(5 + -2x) = 0Subproblem 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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {1, 2.5}
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