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Simplifying (3x + 1)(x + 1) = 34x + -74 Reorder the terms: (1 + 3x)(x + 1) = 34x + -74 Reorder the terms: (1 + 3x)(1 + x) = 34x + -74 Multiply (1 + 3x) * (1 + x) (1(1 + x) + 3x * (1 + x)) = 34x + -74 ((1 * 1 + x * 1) + 3x * (1 + x)) = 34x + -74 ((1 + 1x) + 3x * (1 + x)) = 34x + -74 (1 + 1x + (1 * 3x + x * 3x)) = 34x + -74 (1 + 1x + (3x + 3x2)) = 34x + -74 Combine like terms: 1x + 3x = 4x (1 + 4x + 3x2) = 34x + -74 Reorder the terms: 1 + 4x + 3x2 = -74 + 34x Solving 1 + 4x + 3x2 = -74 + 34x Solving for variable 'x'. Reorder the terms: 1 + 74 + 4x + -34x + 3x2 = -74 + 34x + 74 + -34x Combine like terms: 1 + 74 = 75 75 + 4x + -34x + 3x2 = -74 + 34x + 74 + -34x Combine like terms: 4x + -34x = -30x 75 + -30x + 3x2 = -74 + 34x + 74 + -34x Reorder the terms: 75 + -30x + 3x2 = -74 + 74 + 34x + -34x Combine like terms: -74 + 74 = 0 75 + -30x + 3x2 = 0 + 34x + -34x 75 + -30x + 3x2 = 34x + -34x Combine like terms: 34x + -34x = 0 75 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -10x + x2) = 0 Factor a trinomial. 3((5 + -1x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {5, 5}
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