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Simplifying x3 + 4x2 = x3 + -2x2 + -17x + -5 Reorder the terms: 4x2 + x3 = x3 + -2x2 + -17x + -5 Reorder the terms: 4x2 + x3 = -5 + -17x + -2x2 + x3 Add '-1x3' to each side of the equation. 4x2 + x3 + -1x3 = -5 + -17x + -2x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 4x2 + 0 = -5 + -17x + -2x2 + x3 + -1x3 4x2 = -5 + -17x + -2x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 4x2 = -5 + -17x + -2x2 + 0 4x2 = -5 + -17x + -2x2 Solving 4x2 = -5 + -17x + -2x2 Solving for variable 'x'. Reorder the terms: 5 + 17x + 4x2 + 2x2 = -5 + -17x + -2x2 + 5 + 17x + 2x2 Combine like terms: 4x2 + 2x2 = 6x2 5 + 17x + 6x2 = -5 + -17x + -2x2 + 5 + 17x + 2x2 Reorder the terms: 5 + 17x + 6x2 = -5 + 5 + -17x + 17x + -2x2 + 2x2 Combine like terms: -5 + 5 = 0 5 + 17x + 6x2 = 0 + -17x + 17x + -2x2 + 2x2 5 + 17x + 6x2 = -17x + 17x + -2x2 + 2x2 Combine like terms: -17x + 17x = 0 5 + 17x + 6x2 = 0 + -2x2 + 2x2 5 + 17x + 6x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 5 + 17x + 6x2 = 0 Factor a trinomial. (5 + 2x)(1 + 3x) = 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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-2.5, -0.3333333333}
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