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Simplifying (2x + 1.5)(2x + 4) = 26 Reorder the terms: (1.5 + 2x)(2x + 4) = 26 Reorder the terms: (1.5 + 2x)(4 + 2x) = 26 Multiply (1.5 + 2x) * (4 + 2x) (1.5(4 + 2x) + 2x * (4 + 2x)) = 26 ((4 * 1.5 + 2x * 1.5) + 2x * (4 + 2x)) = 26 ((6 + 3x) + 2x * (4 + 2x)) = 26 (6 + 3x + (4 * 2x + 2x * 2x)) = 26 (6 + 3x + (8x + 4x2)) = 26 Combine like terms: 3x + 8x = 11x (6 + 11x + 4x2) = 26 Solving 6 + 11x + 4x2 = 26 Solving for variable 'x'. Reorder the terms: 6 + -26 + 11x + 4x2 = 26 + -26 Combine like terms: 6 + -26 = -20 -20 + 11x + 4x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -20 + 11x + 4x2 = 0 Factor a trinomial. (-4 + -1x)(5 + -4x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Solution
x = {-4, 1.25}
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