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Simplifying 0 = x2 + 29x + 100 Reorder the terms: 0 = 100 + 29x + x2 Solving 0 = 100 + 29x + x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -29x + -1x2 = 100 + 29x + x2 + -100 + -29x + -1x2 Reorder the terms: -100 + -29x + -1x2 = 100 + -100 + 29x + -29x + x2 + -1x2 Combine like terms: 100 + -100 = 0 -100 + -29x + -1x2 = 0 + 29x + -29x + x2 + -1x2 -100 + -29x + -1x2 = 29x + -29x + x2 + -1x2 Combine like terms: 29x + -29x = 0 -100 + -29x + -1x2 = 0 + x2 + -1x2 -100 + -29x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -100 + -29x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 29x + x2) = 0 Factor a trinomial. -1((25 + x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + x)' equal to zero and attempt to solve: Simplifying 25 + x = 0 Solving 25 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + x = 0 + -25 x = 0 + -25 Combine like terms: 0 + -25 = -25 x = -25 Simplifying x = -25Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-25, -4}
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