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Simplifying 2x2 + 7x + -25 = x2 + 23x + -40 Reorder the terms: -25 + 7x + 2x2 = x2 + 23x + -40 Reorder the terms: -25 + 7x + 2x2 = -40 + 23x + x2 Solving -25 + 7x + 2x2 = -40 + 23x + x2 Solving for variable 'x'. Reorder the terms: -25 + 40 + 7x + -23x + 2x2 + -1x2 = -40 + 23x + x2 + 40 + -23x + -1x2 Combine like terms: -25 + 40 = 15 15 + 7x + -23x + 2x2 + -1x2 = -40 + 23x + x2 + 40 + -23x + -1x2 Combine like terms: 7x + -23x = -16x 15 + -16x + 2x2 + -1x2 = -40 + 23x + x2 + 40 + -23x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 15 + -16x + 1x2 = -40 + 23x + x2 + 40 + -23x + -1x2 Reorder the terms: 15 + -16x + 1x2 = -40 + 40 + 23x + -23x + x2 + -1x2 Combine like terms: -40 + 40 = 0 15 + -16x + 1x2 = 0 + 23x + -23x + x2 + -1x2 15 + -16x + 1x2 = 23x + -23x + x2 + -1x2 Combine like terms: 23x + -23x = 0 15 + -16x + 1x2 = 0 + x2 + -1x2 15 + -16x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + -16x + 1x2 = 0 Factor a trinomial. (1 + -1x)(15 + -1x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {1, 15}
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