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Simplifying (5x + 1)(5x + 1) + -12(5x + 1) + 36 = 0 Reorder the terms: (1 + 5x)(5x + 1) + -12(5x + 1) + 36 = 0 Reorder the terms: (1 + 5x)(1 + 5x) + -12(5x + 1) + 36 = 0 Multiply (1 + 5x) * (1 + 5x) (1(1 + 5x) + 5x * (1 + 5x)) + -12(5x + 1) + 36 = 0 ((1 * 1 + 5x * 1) + 5x * (1 + 5x)) + -12(5x + 1) + 36 = 0 ((1 + 5x) + 5x * (1 + 5x)) + -12(5x + 1) + 36 = 0 (1 + 5x + (1 * 5x + 5x * 5x)) + -12(5x + 1) + 36 = 0 (1 + 5x + (5x + 25x2)) + -12(5x + 1) + 36 = 0 Combine like terms: 5x + 5x = 10x (1 + 10x + 25x2) + -12(5x + 1) + 36 = 0 Reorder the terms: 1 + 10x + 25x2 + -12(1 + 5x) + 36 = 0 1 + 10x + 25x2 + (1 * -12 + 5x * -12) + 36 = 0 1 + 10x + 25x2 + (-12 + -60x) + 36 = 0 Reorder the terms: 1 + -12 + 36 + 10x + -60x + 25x2 = 0 Combine like terms: 1 + -12 = -11 -11 + 36 + 10x + -60x + 25x2 = 0 Combine like terms: -11 + 36 = 25 25 + 10x + -60x + 25x2 = 0 Combine like terms: 10x + -60x = -50x 25 + -50x + 25x2 = 0 Solving 25 + -50x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(1 + -2x + x2) = 0 Factor a trinomial. 25((1 + -1x)(1 + -1x)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1, 1}
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