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Simplifying 2x2 + 2x + 57 = (x + 6)(x + 6) Reorder the terms: 57 + 2x + 2x2 = (x + 6)(x + 6) Reorder the terms: 57 + 2x + 2x2 = (6 + x)(x + 6) Reorder the terms: 57 + 2x + 2x2 = (6 + x)(6 + x) Multiply (6 + x) * (6 + x) 57 + 2x + 2x2 = (6(6 + x) + x(6 + x)) 57 + 2x + 2x2 = ((6 * 6 + x * 6) + x(6 + x)) 57 + 2x + 2x2 = ((36 + 6x) + x(6 + x)) 57 + 2x + 2x2 = (36 + 6x + (6 * x + x * x)) 57 + 2x + 2x2 = (36 + 6x + (6x + x2)) Combine like terms: 6x + 6x = 12x 57 + 2x + 2x2 = (36 + 12x + x2) Solving 57 + 2x + 2x2 = 36 + 12x + x2 Solving for variable 'x'. Reorder the terms: 57 + -36 + 2x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 57 + -36 = 21 21 + 2x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 2x + -12x = -10x 21 + -10x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 21 + -10x + 1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Reorder the terms: 21 + -10x + 1x2 = 36 + -36 + 12x + -12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 21 + -10x + 1x2 = 0 + 12x + -12x + x2 + -1x2 21 + -10x + 1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 21 + -10x + 1x2 = 0 + x2 + -1x2 21 + -10x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -10x + 1x2 = 0 Factor a trinomial. (3 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {3, 7}
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