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Simplifying (4x + -1)(4x + -1) = 20x + -5 Reorder the terms: (-1 + 4x)(4x + -1) = 20x + -5 Reorder the terms: (-1 + 4x)(-1 + 4x) = 20x + -5 Multiply (-1 + 4x) * (-1 + 4x) (-1(-1 + 4x) + 4x * (-1 + 4x)) = 20x + -5 ((-1 * -1 + 4x * -1) + 4x * (-1 + 4x)) = 20x + -5 ((1 + -4x) + 4x * (-1 + 4x)) = 20x + -5 (1 + -4x + (-1 * 4x + 4x * 4x)) = 20x + -5 (1 + -4x + (-4x + 16x2)) = 20x + -5 Combine like terms: -4x + -4x = -8x (1 + -8x + 16x2) = 20x + -5 Reorder the terms: 1 + -8x + 16x2 = -5 + 20x Solving 1 + -8x + 16x2 = -5 + 20x Solving for variable 'x'. Reorder the terms: 1 + 5 + -8x + -20x + 16x2 = -5 + 20x + 5 + -20x Combine like terms: 1 + 5 = 6 6 + -8x + -20x + 16x2 = -5 + 20x + 5 + -20x Combine like terms: -8x + -20x = -28x 6 + -28x + 16x2 = -5 + 20x + 5 + -20x Reorder the terms: 6 + -28x + 16x2 = -5 + 5 + 20x + -20x Combine like terms: -5 + 5 = 0 6 + -28x + 16x2 = 0 + 20x + -20x 6 + -28x + 16x2 = 20x + -20x Combine like terms: 20x + -20x = 0 6 + -28x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -14x + 8x2) = 0 Factor a trinomial. 2((1 + -4x)(3 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0.25, 1.5}
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