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Simplifying 0 = 4x2 + 16x + 7 Reorder the terms: 0 = 7 + 16x + 4x2 Solving 0 = 7 + 16x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -16x + -4x2 = 7 + 16x + 4x2 + -7 + -16x + -4x2 Reorder the terms: -7 + -16x + -4x2 = 7 + -7 + 16x + -16x + 4x2 + -4x2 Combine like terms: 7 + -7 = 0 -7 + -16x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2 -7 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -7 + -16x + -4x2 = 0 + 4x2 + -4x2 -7 + -16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -7 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 16x + 4x2) = 0 Factor a trinomial. -1((7 + 2x)(1 + 2x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 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 = {-3.5, -0.5}
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