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Simplifying 12 + 4x2 + -6 + 2x + x2 = 78 Reorder the terms: 12 + -6 + 2x + 4x2 + x2 = 78 Combine like terms: 12 + -6 = 6 6 + 2x + 4x2 + x2 = 78 Combine like terms: 4x2 + x2 = 5x2 6 + 2x + 5x2 = 78 Solving 6 + 2x + 5x2 = 78 Solving for variable 'x'. Reorder the terms: 6 + -78 + 2x + 5x2 = 78 + -78 Combine like terms: 6 + -78 = -72 -72 + 2x + 5x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -72 + 2x + 5x2 = 0 Factor a trinomial. (-4 + -1x)(18 + -5x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(18 + -5x)' equal to zero and attempt to solve: Simplifying 18 + -5x = 0 Solving 18 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -5x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -5x = 0 + -18 -5x = 0 + -18 Combine like terms: 0 + -18 = -18 -5x = -18 Divide each side by '-5'. x = 3.6 Simplifying x = 3.6Solution
x = {-4, 3.6}
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