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Simplifying 1x2 + (2x + 20)(2x + 20) = (2x + 22)(2x + 22) Reorder the terms: 1x2 + (20 + 2x)(2x + 20) = (2x + 22)(2x + 22) Reorder the terms: 1x2 + (20 + 2x)(20 + 2x) = (2x + 22)(2x + 22) Multiply (20 + 2x) * (20 + 2x) 1x2 + (20(20 + 2x) + 2x * (20 + 2x)) = (2x + 22)(2x + 22) 1x2 + ((20 * 20 + 2x * 20) + 2x * (20 + 2x)) = (2x + 22)(2x + 22) 1x2 + ((400 + 40x) + 2x * (20 + 2x)) = (2x + 22)(2x + 22) 1x2 + (400 + 40x + (20 * 2x + 2x * 2x)) = (2x + 22)(2x + 22) 1x2 + (400 + 40x + (40x + 4x2)) = (2x + 22)(2x + 22) Combine like terms: 40x + 40x = 80x 1x2 + (400 + 80x + 4x2) = (2x + 22)(2x + 22) Reorder the terms: 400 + 80x + 1x2 + 4x2 = (2x + 22)(2x + 22) Combine like terms: 1x2 + 4x2 = 5x2 400 + 80x + 5x2 = (2x + 22)(2x + 22) Reorder the terms: 400 + 80x + 5x2 = (22 + 2x)(2x + 22) Reorder the terms: 400 + 80x + 5x2 = (22 + 2x)(22 + 2x) Multiply (22 + 2x) * (22 + 2x) 400 + 80x + 5x2 = (22(22 + 2x) + 2x * (22 + 2x)) 400 + 80x + 5x2 = ((22 * 22 + 2x * 22) + 2x * (22 + 2x)) 400 + 80x + 5x2 = ((484 + 44x) + 2x * (22 + 2x)) 400 + 80x + 5x2 = (484 + 44x + (22 * 2x + 2x * 2x)) 400 + 80x + 5x2 = (484 + 44x + (44x + 4x2)) Combine like terms: 44x + 44x = 88x 400 + 80x + 5x2 = (484 + 88x + 4x2) Solving 400 + 80x + 5x2 = 484 + 88x + 4x2 Solving for variable 'x'. Reorder the terms: 400 + -484 + 80x + -88x + 5x2 + -4x2 = 484 + 88x + 4x2 + -484 + -88x + -4x2 Combine like terms: 400 + -484 = -84 -84 + 80x + -88x + 5x2 + -4x2 = 484 + 88x + 4x2 + -484 + -88x + -4x2 Combine like terms: 80x + -88x = -8x -84 + -8x + 5x2 + -4x2 = 484 + 88x + 4x2 + -484 + -88x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 -84 + -8x + 1x2 = 484 + 88x + 4x2 + -484 + -88x + -4x2 Reorder the terms: -84 + -8x + 1x2 = 484 + -484 + 88x + -88x + 4x2 + -4x2 Combine like terms: 484 + -484 = 0 -84 + -8x + 1x2 = 0 + 88x + -88x + 4x2 + -4x2 -84 + -8x + 1x2 = 88x + -88x + 4x2 + -4x2 Combine like terms: 88x + -88x = 0 -84 + -8x + 1x2 = 0 + 4x2 + -4x2 -84 + -8x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -84 + -8x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(14 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-6, 14}
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