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Simplifying 5 + x = 4x2 + 17x + -4 Reorder the terms: 5 + x = -4 + 17x + 4x2 Solving 5 + x = -4 + 17x + 4x2 Solving for variable 'x'. Reorder the terms: 5 + 4 + x + -17x + -4x2 = -4 + 17x + 4x2 + 4 + -17x + -4x2 Combine like terms: 5 + 4 = 9 9 + x + -17x + -4x2 = -4 + 17x + 4x2 + 4 + -17x + -4x2 Combine like terms: x + -17x = -16x 9 + -16x + -4x2 = -4 + 17x + 4x2 + 4 + -17x + -4x2 Reorder the terms: 9 + -16x + -4x2 = -4 + 4 + 17x + -17x + 4x2 + -4x2 Combine like terms: -4 + 4 = 0 9 + -16x + -4x2 = 0 + 17x + -17x + 4x2 + -4x2 9 + -16x + -4x2 = 17x + -17x + 4x2 + -4x2 Combine like terms: 17x + -17x = 0 9 + -16x + -4x2 = 0 + 4x2 + -4x2 9 + -16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 9 + -16x + -4x2 = 0 Factor a trinomial. (1 + -2x)(9 + 2x) = 0Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Solution
x = {0.5, -4.5}
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