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Simplifying x2 + (11 + x)(11 + x) = (2x + -11)(2x + -11) Multiply (11 + x) * (11 + x) x2 + (11(11 + x) + x(11 + x)) = (2x + -11)(2x + -11) x2 + ((11 * 11 + x * 11) + x(11 + x)) = (2x + -11)(2x + -11) x2 + ((121 + 11x) + x(11 + x)) = (2x + -11)(2x + -11) x2 + (121 + 11x + (11 * x + x * x)) = (2x + -11)(2x + -11) x2 + (121 + 11x + (11x + x2)) = (2x + -11)(2x + -11) Combine like terms: 11x + 11x = 22x x2 + (121 + 22x + x2) = (2x + -11)(2x + -11) Reorder the terms: 121 + 22x + x2 + x2 = (2x + -11)(2x + -11) Combine like terms: x2 + x2 = 2x2 121 + 22x + 2x2 = (2x + -11)(2x + -11) Reorder the terms: 121 + 22x + 2x2 = (-11 + 2x)(2x + -11) Reorder the terms: 121 + 22x + 2x2 = (-11 + 2x)(-11 + 2x) Multiply (-11 + 2x) * (-11 + 2x) 121 + 22x + 2x2 = (-11(-11 + 2x) + 2x * (-11 + 2x)) 121 + 22x + 2x2 = ((-11 * -11 + 2x * -11) + 2x * (-11 + 2x)) 121 + 22x + 2x2 = ((121 + -22x) + 2x * (-11 + 2x)) 121 + 22x + 2x2 = (121 + -22x + (-11 * 2x + 2x * 2x)) 121 + 22x + 2x2 = (121 + -22x + (-22x + 4x2)) Combine like terms: -22x + -22x = -44x 121 + 22x + 2x2 = (121 + -44x + 4x2) Add '-121' to each side of the equation. 121 + 22x + -121 + 2x2 = 121 + -44x + -121 + 4x2 Reorder the terms: 121 + -121 + 22x + 2x2 = 121 + -44x + -121 + 4x2 Combine like terms: 121 + -121 = 0 0 + 22x + 2x2 = 121 + -44x + -121 + 4x2 22x + 2x2 = 121 + -44x + -121 + 4x2 Reorder the terms: 22x + 2x2 = 121 + -121 + -44x + 4x2 Combine like terms: 121 + -121 = 0 22x + 2x2 = 0 + -44x + 4x2 22x + 2x2 = -44x + 4x2 Solving 22x + 2x2 = -44x + 4x2 Solving for variable 'x'. Reorder the terms: 22x + 44x + 2x2 + -4x2 = -44x + 4x2 + 44x + -4x2 Combine like terms: 22x + 44x = 66x 66x + 2x2 + -4x2 = -44x + 4x2 + 44x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 66x + -2x2 = -44x + 4x2 + 44x + -4x2 Reorder the terms: 66x + -2x2 = -44x + 44x + 4x2 + -4x2 Combine like terms: -44x + 44x = 0 66x + -2x2 = 0 + 4x2 + -4x2 66x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 66x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(33 + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(33 + -1x)' equal to zero and attempt to solve: Simplifying 33 + -1x = 0 Solving 33 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -1x = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -1x = 0 + -33 -1x = 0 + -33 Combine like terms: 0 + -33 = -33 -1x = -33 Divide each side by '-1'. x = 33 Simplifying x = 33Solution
x = {0, 33}
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