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Simplifying 6x2 = 10x + 84 Reorder the terms: 6x2 = 84 + 10x Solving 6x2 = 84 + 10x Solving for variable 'x'. Reorder the terms: -84 + -10x + 6x2 = 84 + 10x + -84 + -10x Reorder the terms: -84 + -10x + 6x2 = 84 + -84 + 10x + -10x Combine like terms: 84 + -84 = 0 -84 + -10x + 6x2 = 0 + 10x + -10x -84 + -10x + 6x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -84 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -5x + 3x2) = 0 Factor a trinomial. 2((-3 + -1x)(14 + -3x)) = 0 Ignore the factor 2.Subproblem 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 '(14 + -3x)' equal to zero and attempt to solve: Simplifying 14 + -3x = 0 Solving 14 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -3x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -3x = 0 + -14 -3x = 0 + -14 Combine like terms: 0 + -14 = -14 -3x = -14 Divide each side by '-3'. x = 4.666666667 Simplifying x = 4.666666667Solution
x = {-3, 4.666666667}
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