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Simplifying -6x2 = 41x + 63 Reorder the terms: -6x2 = 63 + 41x Solving -6x2 = 63 + 41x Solving for variable 'x'. Reorder the terms: -63 + -41x + -6x2 = 63 + 41x + -63 + -41x Reorder the terms: -63 + -41x + -6x2 = 63 + -63 + 41x + -41x Combine like terms: 63 + -63 = 0 -63 + -41x + -6x2 = 0 + 41x + -41x -63 + -41x + -6x2 = 41x + -41x Combine like terms: 41x + -41x = 0 -63 + -41x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(63 + 41x + 6x2) = 0 Factor a trinomial. -1((9 + 2x)(7 + 3x)) = 0 Ignore the factor -1.Subproblem 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 '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 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 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Solution
x = {-4.5, -2.333333333}
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