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Simplifying 10X2 + 5 = -15X Reorder the terms: 5 + 10X2 = -15X Solving 5 + 10X2 = -15X Solving for variable 'X'. Reorder the terms: 5 + 15X + 10X2 = -15X + 15X Combine like terms: -15X + 15X = 0 5 + 15X + 10X2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 3X + 2X2) = 0 Factor a trinomial. 5((1 + X)(1 + 2X)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + X)' equal to zero and attempt to solve: Simplifying 1 + X = 0 Solving 1 + X = 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 + X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + X = 0 + -1 X = 0 + -1 Combine like terms: 0 + -1 = -1 X = -1 Simplifying X = -1Subproblem 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 = {-1, -0.5}
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