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Simplifying 5 + -3x + 4x2 + 7x + -5x2 = 0 Reorder the terms: 5 + -3x + 7x + 4x2 + -5x2 = 0 Combine like terms: -3x + 7x = 4x 5 + 4x + 4x2 + -5x2 = 0 Combine like terms: 4x2 + -5x2 = -1x2 5 + 4x + -1x2 = 0 Solving 5 + 4x + -1x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + -1x)(1 + x) = 0Subproblem 1
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 = 5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {5, -1}
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