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Simplifying (-13x2 + 7x) + -1(5x2 + 10x + -3) = 0 Reorder the terms: (7x + -13x2) + -1(5x2 + 10x + -3) = 0 Remove parenthesis around (7x + -13x2) 7x + -13x2 + -1(5x2 + 10x + -3) = 0 Reorder the terms: 7x + -13x2 + -1(-3 + 10x + 5x2) = 0 7x + -13x2 + (-3 * -1 + 10x * -1 + 5x2 * -1) = 0 7x + -13x2 + (3 + -10x + -5x2) = 0 Reorder the terms: 3 + 7x + -10x + -13x2 + -5x2 = 0 Combine like terms: 7x + -10x = -3x 3 + -3x + -13x2 + -5x2 = 0 Combine like terms: -13x2 + -5x2 = -18x2 3 + -3x + -18x2 = 0 Solving 3 + -3x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -1x + -6x2) = 0 Factor a trinomial. 3((1 + -3x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
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 = 0.3333333333Subproblem 2
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 = -0.5Solution
x = {0.3333333333, -0.5}
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