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Simplifying (5x2 + -4x + 4) + -1(3x2 + 5x + -6) = 0 Reorder the terms: (4 + -4x + 5x2) + -1(3x2 + 5x + -6) = 0 Remove parenthesis around (4 + -4x + 5x2) 4 + -4x + 5x2 + -1(3x2 + 5x + -6) = 0 Reorder the terms: 4 + -4x + 5x2 + -1(-6 + 5x + 3x2) = 0 4 + -4x + 5x2 + (-6 * -1 + 5x * -1 + 3x2 * -1) = 0 4 + -4x + 5x2 + (6 + -5x + -3x2) = 0 Reorder the terms: 4 + 6 + -4x + -5x + 5x2 + -3x2 = 0 Combine like terms: 4 + 6 = 10 10 + -4x + -5x + 5x2 + -3x2 = 0 Combine like terms: -4x + -5x = -9x 10 + -9x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 10 + -9x + 2x2 = 0 Solving 10 + -9x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (2 + -1x)(5 + -2x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
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 = 2.5Solution
x = {2, 2.5}
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