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Simplifying (x + 7)(x + 5) = x2 + px + 35 Reorder the terms: (7 + x)(x + 5) = x2 + px + 35 Reorder the terms: (7 + x)(5 + x) = x2 + px + 35 Multiply (7 + x) * (5 + x) (7(5 + x) + x(5 + x)) = x2 + px + 35 ((5 * 7 + x * 7) + x(5 + x)) = x2 + px + 35 ((35 + 7x) + x(5 + x)) = x2 + px + 35 (35 + 7x + (5 * x + x * x)) = x2 + px + 35 (35 + 7x + (5x + x2)) = x2 + px + 35 Combine like terms: 7x + 5x = 12x (35 + 12x + x2) = x2 + px + 35 Reorder the terms: 35 + 12x + x2 = 35 + px + x2 Add '-35' to each side of the equation. 35 + 12x + -35 + x2 = 35 + px + -35 + x2 Reorder the terms: 35 + -35 + 12x + x2 = 35 + px + -35 + x2 Combine like terms: 35 + -35 = 0 0 + 12x + x2 = 35 + px + -35 + x2 12x + x2 = 35 + px + -35 + x2 Reorder the terms: 12x + x2 = 35 + -35 + px + x2 Combine like terms: 35 + -35 = 0 12x + x2 = 0 + px + x2 12x + x2 = px + x2 Add '-1x2' to each side of the equation. 12x + x2 + -1x2 = px + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12x + 0 = px + x2 + -1x2 12x = px + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12x = px + 0 12x = px Solving 12x = px Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1px' to each side of the equation. -1px + 12x = px + -1px Combine like terms: px + -1px = 0 -1px + 12x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1p + 12) = 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 '(-1p + 12)' equal to zero and attempt to solve: Simplifying -1p + 12 = 0 Reorder the terms: 12 + -1p = 0 Solving 12 + -1p = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1p = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1p = 0 + -12 -1p = 0 + -12 Combine like terms: 0 + -12 = -12 -1p = -12 Add 'p' to each side of the equation. -1p + p = -12 + p Combine like terms: -1p + p = 0 0 = -12 + p Simplifying 0 = -12 + p The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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