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Simplifying (3x2 + -5x + 1) + -1(x2 + -7x + 5) = 0 Reorder the terms: (1 + -5x + 3x2) + -1(x2 + -7x + 5) = 0 Remove parenthesis around (1 + -5x + 3x2) 1 + -5x + 3x2 + -1(x2 + -7x + 5) = 0 Reorder the terms: 1 + -5x + 3x2 + -1(5 + -7x + x2) = 0 1 + -5x + 3x2 + (5 * -1 + -7x * -1 + x2 * -1) = 0 1 + -5x + 3x2 + (-5 + 7x + -1x2) = 0 Reorder the terms: 1 + -5 + -5x + 7x + 3x2 + -1x2 = 0 Combine like terms: 1 + -5 = -4 -4 + -5x + 7x + 3x2 + -1x2 = 0 Combine like terms: -5x + 7x = 2x -4 + 2x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -4 + 2x + 2x2 = 0 Solving -4 + 2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x + x2) = 0 Factor a trinomial. 2((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2, 1}
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