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Simplifying 0 = 5X2 + 7X + 2 Reorder the terms: 0 = 2 + 7X + 5X2 Solving 0 = 2 + 7X + 5X2 Solving for variable 'X'. Combine like terms: 0 + -2 = -2 -2 + -7X + -5X2 = 2 + 7X + 5X2 + -2 + -7X + -5X2 Reorder the terms: -2 + -7X + -5X2 = 2 + -2 + 7X + -7X + 5X2 + -5X2 Combine like terms: 2 + -2 = 0 -2 + -7X + -5X2 = 0 + 7X + -7X + 5X2 + -5X2 -2 + -7X + -5X2 = 7X + -7X + 5X2 + -5X2 Combine like terms: 7X + -7X = 0 -2 + -7X + -5X2 = 0 + 5X2 + -5X2 -2 + -7X + -5X2 = 5X2 + -5X2 Combine like terms: 5X2 + -5X2 = 0 -2 + -7X + -5X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 7X + 5X2) = 0 Factor a trinomial. -1((1 + X)(2 + 5X)) = 0 Ignore the factor -1.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 '(2 + 5X)' equal to zero and attempt to solve: Simplifying 2 + 5X = 0 Solving 2 + 5X = 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 + 5X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5X = 0 + -2 5X = 0 + -2 Combine like terms: 0 + -2 = -2 5X = -2 Divide each side by '5'. X = -0.4 Simplifying X = -0.4Solution
X = {-1, -0.4}
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