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Simplifying (2x + 5)(2x + 5) = x + 13 Reorder the terms: (5 + 2x)(2x + 5) = x + 13 Reorder the terms: (5 + 2x)(5 + 2x) = x + 13 Multiply (5 + 2x) * (5 + 2x) (5(5 + 2x) + 2x * (5 + 2x)) = x + 13 ((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = x + 13 ((25 + 10x) + 2x * (5 + 2x)) = x + 13 (25 + 10x + (5 * 2x + 2x * 2x)) = x + 13 (25 + 10x + (10x + 4x2)) = x + 13 Combine like terms: 10x + 10x = 20x (25 + 20x + 4x2) = x + 13 Reorder the terms: 25 + 20x + 4x2 = 13 + x Solving 25 + 20x + 4x2 = 13 + x Solving for variable 'x'. Reorder the terms: 25 + -13 + 20x + -1x + 4x2 = 13 + x + -13 + -1x Combine like terms: 25 + -13 = 12 12 + 20x + -1x + 4x2 = 13 + x + -13 + -1x Combine like terms: 20x + -1x = 19x 12 + 19x + 4x2 = 13 + x + -13 + -1x Reorder the terms: 12 + 19x + 4x2 = 13 + -13 + x + -1x Combine like terms: 13 + -13 = 0 12 + 19x + 4x2 = 0 + x + -1x 12 + 19x + 4x2 = x + -1x Combine like terms: x + -1x = 0 12 + 19x + 4x2 = 0 Factor a trinomial. (4 + x)(3 + 4x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-4, -0.75}
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