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Simplifying 7x2 + 20x + 17 = -1x2 + 55x + 42 Reorder the terms: 17 + 20x + 7x2 = -1x2 + 55x + 42 Reorder the terms: 17 + 20x + 7x2 = 42 + 55x + -1x2 Solving 17 + 20x + 7x2 = 42 + 55x + -1x2 Solving for variable 'x'. Reorder the terms: 17 + -42 + 20x + -55x + 7x2 + x2 = 42 + 55x + -1x2 + -42 + -55x + x2 Combine like terms: 17 + -42 = -25 -25 + 20x + -55x + 7x2 + x2 = 42 + 55x + -1x2 + -42 + -55x + x2 Combine like terms: 20x + -55x = -35x -25 + -35x + 7x2 + x2 = 42 + 55x + -1x2 + -42 + -55x + x2 Combine like terms: 7x2 + x2 = 8x2 -25 + -35x + 8x2 = 42 + 55x + -1x2 + -42 + -55x + x2 Reorder the terms: -25 + -35x + 8x2 = 42 + -42 + 55x + -55x + -1x2 + x2 Combine like terms: 42 + -42 = 0 -25 + -35x + 8x2 = 0 + 55x + -55x + -1x2 + x2 -25 + -35x + 8x2 = 55x + -55x + -1x2 + x2 Combine like terms: 55x + -55x = 0 -25 + -35x + 8x2 = 0 + -1x2 + x2 -25 + -35x + 8x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -25 + -35x + 8x2 = 0 Factor a trinomial. (-5 + -8x)(5 + -1x) = 0Subproblem 1
Set the factor '(-5 + -8x)' equal to zero and attempt to solve: Simplifying -5 + -8x = 0 Solving -5 + -8x = 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 + -8x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8x = 0 + 5 -8x = 0 + 5 Combine like terms: 0 + 5 = 5 -8x = 5 Divide each side by '-8'. x = -0.625 Simplifying x = -0.625Subproblem 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 = {-0.625, 5}
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