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Simplifying 6x2 + 23x + 176 = 180 Reorder the terms: 176 + 23x + 6x2 = 180 Solving 176 + 23x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: 176 + -180 + 23x + 6x2 = 180 + -180 Combine like terms: 176 + -180 = -4 -4 + 23x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -4 + 23x + 6x2 = 0 Factor a trinomial. (-4 + -1x)(1 + -6x) = 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 '(1 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 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 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Divide each side by '-6'. x = 0.1666666667 Simplifying x = 0.1666666667Solution
x = {-4, 0.1666666667}
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