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Simplifying 14x2 + -22x + 8 = 2x2 + -6x + 3 Reorder the terms: 8 + -22x + 14x2 = 2x2 + -6x + 3 Reorder the terms: 8 + -22x + 14x2 = 3 + -6x + 2x2 Solving 8 + -22x + 14x2 = 3 + -6x + 2x2 Solving for variable 'x'. Reorder the terms: 8 + -3 + -22x + 6x + 14x2 + -2x2 = 3 + -6x + 2x2 + -3 + 6x + -2x2 Combine like terms: 8 + -3 = 5 5 + -22x + 6x + 14x2 + -2x2 = 3 + -6x + 2x2 + -3 + 6x + -2x2 Combine like terms: -22x + 6x = -16x 5 + -16x + 14x2 + -2x2 = 3 + -6x + 2x2 + -3 + 6x + -2x2 Combine like terms: 14x2 + -2x2 = 12x2 5 + -16x + 12x2 = 3 + -6x + 2x2 + -3 + 6x + -2x2 Reorder the terms: 5 + -16x + 12x2 = 3 + -3 + -6x + 6x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 5 + -16x + 12x2 = 0 + -6x + 6x + 2x2 + -2x2 5 + -16x + 12x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 5 + -16x + 12x2 = 0 + 2x2 + -2x2 5 + -16x + 12x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + -16x + 12x2 = 0 Factor a trinomial. (1 + -2x)(5 + -6x) = 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 '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 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 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {0.5, 0.8333333333}
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