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Simplifying 11x2 + 29x + -30 = -3x2 + 6x Reorder the terms: -30 + 29x + 11x2 = -3x2 + 6x Reorder the terms: -30 + 29x + 11x2 = 6x + -3x2 Solving -30 + 29x + 11x2 = 6x + -3x2 Solving for variable 'x'. Reorder the terms: -30 + 29x + -6x + 11x2 + 3x2 = 6x + -3x2 + -6x + 3x2 Combine like terms: 29x + -6x = 23x -30 + 23x + 11x2 + 3x2 = 6x + -3x2 + -6x + 3x2 Combine like terms: 11x2 + 3x2 = 14x2 -30 + 23x + 14x2 = 6x + -3x2 + -6x + 3x2 Reorder the terms: -30 + 23x + 14x2 = 6x + -6x + -3x2 + 3x2 Combine like terms: 6x + -6x = 0 -30 + 23x + 14x2 = 0 + -3x2 + 3x2 -30 + 23x + 14x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -30 + 23x + 14x2 = 0 Factor a trinomial. (-5 + -2x)(6 + -7x) = 0Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 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 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571Solution
x = {-2.5, 0.8571428571}
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