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Simplifying x2 + 3x + 4 = 34 + 10x + -1x2 Reorder the terms: 4 + 3x + x2 = 34 + 10x + -1x2 Solving 4 + 3x + x2 = 34 + 10x + -1x2 Solving for variable 'x'. Reorder the terms: 4 + -34 + 3x + -10x + x2 + x2 = 34 + 10x + -1x2 + -34 + -10x + x2 Combine like terms: 4 + -34 = -30 -30 + 3x + -10x + x2 + x2 = 34 + 10x + -1x2 + -34 + -10x + x2 Combine like terms: 3x + -10x = -7x -30 + -7x + x2 + x2 = 34 + 10x + -1x2 + -34 + -10x + x2 Combine like terms: x2 + x2 = 2x2 -30 + -7x + 2x2 = 34 + 10x + -1x2 + -34 + -10x + x2 Reorder the terms: -30 + -7x + 2x2 = 34 + -34 + 10x + -10x + -1x2 + x2 Combine like terms: 34 + -34 = 0 -30 + -7x + 2x2 = 0 + 10x + -10x + -1x2 + x2 -30 + -7x + 2x2 = 10x + -10x + -1x2 + x2 Combine like terms: 10x + -10x = 0 -30 + -7x + 2x2 = 0 + -1x2 + x2 -30 + -7x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -30 + -7x + 2x2 = 0 Factor a trinomial. (-5 + -2x)(6 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-2.5, 6}
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