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Simplifying 3x2 + 5x + -7 = x2 + 8x + 28 Reorder the terms: -7 + 5x + 3x2 = x2 + 8x + 28 Reorder the terms: -7 + 5x + 3x2 = 28 + 8x + x2 Solving -7 + 5x + 3x2 = 28 + 8x + x2 Solving for variable 'x'. Reorder the terms: -7 + -28 + 5x + -8x + 3x2 + -1x2 = 28 + 8x + x2 + -28 + -8x + -1x2 Combine like terms: -7 + -28 = -35 -35 + 5x + -8x + 3x2 + -1x2 = 28 + 8x + x2 + -28 + -8x + -1x2 Combine like terms: 5x + -8x = -3x -35 + -3x + 3x2 + -1x2 = 28 + 8x + x2 + -28 + -8x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -35 + -3x + 2x2 = 28 + 8x + x2 + -28 + -8x + -1x2 Reorder the terms: -35 + -3x + 2x2 = 28 + -28 + 8x + -8x + x2 + -1x2 Combine like terms: 28 + -28 = 0 -35 + -3x + 2x2 = 0 + 8x + -8x + x2 + -1x2 -35 + -3x + 2x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -35 + -3x + 2x2 = 0 + x2 + -1x2 -35 + -3x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -35 + -3x + 2x2 = 0 Factor a trinomial. (-7 + -2x)(5 + -1x) = 0Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-3.5, 5}
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