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Simplifying 5(4x2 + 4x + 1) + -1(2x + 1)(x + -1) = 0 Reorder the terms: 5(1 + 4x + 4x2) + -1(2x + 1)(x + -1) = 0 (1 * 5 + 4x * 5 + 4x2 * 5) + -1(2x + 1)(x + -1) = 0 (5 + 20x + 20x2) + -1(2x + 1)(x + -1) = 0 Reorder the terms: 5 + 20x + 20x2 + -1(1 + 2x)(x + -1) = 0 Reorder the terms: 5 + 20x + 20x2 + -1(1 + 2x)(-1 + x) = 0 Multiply (1 + 2x) * (-1 + x) 5 + 20x + 20x2 + -1(1(-1 + x) + 2x * (-1 + x)) = 0 5 + 20x + 20x2 + -1((-1 * 1 + x * 1) + 2x * (-1 + x)) = 0 5 + 20x + 20x2 + -1((-1 + 1x) + 2x * (-1 + x)) = 0 5 + 20x + 20x2 + -1(-1 + 1x + (-1 * 2x + x * 2x)) = 0 5 + 20x + 20x2 + -1(-1 + 1x + (-2x + 2x2)) = 0 Combine like terms: 1x + -2x = -1x 5 + 20x + 20x2 + -1(-1 + -1x + 2x2) = 0 5 + 20x + 20x2 + (-1 * -1 + -1x * -1 + 2x2 * -1) = 0 5 + 20x + 20x2 + (1 + 1x + -2x2) = 0 Reorder the terms: 5 + 1 + 20x + 1x + 20x2 + -2x2 = 0 Combine like terms: 5 + 1 = 6 6 + 20x + 1x + 20x2 + -2x2 = 0 Combine like terms: 20x + 1x = 21x 6 + 21x + 20x2 + -2x2 = 0 Combine like terms: 20x2 + -2x2 = 18x2 6 + 21x + 18x2 = 0 Solving 6 + 21x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 7x + 6x2) = 0 Factor a trinomial. 3((2 + 3x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 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 = {-0.6666666667, -0.5}
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