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Simplifying x2 + (35 + -1x)(35 + -1x) = (35 + x)(35 + x) Multiply (35 + -1x) * (35 + -1x) x2 + (35(35 + -1x) + -1x * (35 + -1x)) = (35 + x)(35 + x) x2 + ((35 * 35 + -1x * 35) + -1x * (35 + -1x)) = (35 + x)(35 + x) x2 + ((1225 + -35x) + -1x * (35 + -1x)) = (35 + x)(35 + x) x2 + (1225 + -35x + (35 * -1x + -1x * -1x)) = (35 + x)(35 + x) x2 + (1225 + -35x + (-35x + 1x2)) = (35 + x)(35 + x) Combine like terms: -35x + -35x = -70x x2 + (1225 + -70x + 1x2) = (35 + x)(35 + x) Reorder the terms: 1225 + -70x + x2 + 1x2 = (35 + x)(35 + x) Combine like terms: x2 + 1x2 = 2x2 1225 + -70x + 2x2 = (35 + x)(35 + x) Multiply (35 + x) * (35 + x) 1225 + -70x + 2x2 = (35(35 + x) + x(35 + x)) 1225 + -70x + 2x2 = ((35 * 35 + x * 35) + x(35 + x)) 1225 + -70x + 2x2 = ((1225 + 35x) + x(35 + x)) 1225 + -70x + 2x2 = (1225 + 35x + (35 * x + x * x)) 1225 + -70x + 2x2 = (1225 + 35x + (35x + x2)) Combine like terms: 35x + 35x = 70x 1225 + -70x + 2x2 = (1225 + 70x + x2) Add '-1225' to each side of the equation. 1225 + -70x + -1225 + 2x2 = 1225 + 70x + -1225 + x2 Reorder the terms: 1225 + -1225 + -70x + 2x2 = 1225 + 70x + -1225 + x2 Combine like terms: 1225 + -1225 = 0 0 + -70x + 2x2 = 1225 + 70x + -1225 + x2 -70x + 2x2 = 1225 + 70x + -1225 + x2 Reorder the terms: -70x + 2x2 = 1225 + -1225 + 70x + x2 Combine like terms: 1225 + -1225 = 0 -70x + 2x2 = 0 + 70x + x2 -70x + 2x2 = 70x + x2 Solving -70x + 2x2 = 70x + x2 Solving for variable 'x'. Reorder the terms: -70x + -70x + 2x2 + -1x2 = 70x + x2 + -70x + -1x2 Combine like terms: -70x + -70x = -140x -140x + 2x2 + -1x2 = 70x + x2 + -70x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -140x + 1x2 = 70x + x2 + -70x + -1x2 Reorder the terms: -140x + 1x2 = 70x + -70x + x2 + -1x2 Combine like terms: 70x + -70x = 0 -140x + 1x2 = 0 + x2 + -1x2 -140x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -140x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-140 + x) = 0Subproblem 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 '(-140 + x)' equal to zero and attempt to solve: Simplifying -140 + x = 0 Solving -140 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '140' to each side of the equation. -140 + 140 + x = 0 + 140 Combine like terms: -140 + 140 = 0 0 + x = 0 + 140 x = 0 + 140 Combine like terms: 0 + 140 = 140 x = 140 Simplifying x = 140Solution
x = {0, 140}
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