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Simplifying 2x2 + 17x + 43 = -2x + 1 Reorder the terms: 43 + 17x + 2x2 = -2x + 1 Reorder the terms: 43 + 17x + 2x2 = 1 + -2x Solving 43 + 17x + 2x2 = 1 + -2x Solving for variable 'x'. Reorder the terms: 43 + -1 + 17x + 2x + 2x2 = 1 + -2x + -1 + 2x Combine like terms: 43 + -1 = 42 42 + 17x + 2x + 2x2 = 1 + -2x + -1 + 2x Combine like terms: 17x + 2x = 19x 42 + 19x + 2x2 = 1 + -2x + -1 + 2x Reorder the terms: 42 + 19x + 2x2 = 1 + -1 + -2x + 2x Combine like terms: 1 + -1 = 0 42 + 19x + 2x2 = 0 + -2x + 2x 42 + 19x + 2x2 = -2x + 2x Combine like terms: -2x + 2x = 0 42 + 19x + 2x2 = 0 Factor a trinomial. (6 + x)(7 + 2x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Solution
x = {-6, -3.5}
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