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Simplifying -84 = s(s + 19) Reorder the terms: -84 = s(19 + s) -84 = (19 * s + s * s) -84 = (19s + s2) Solving -84 = 19s + s2 Solving for variable 's'. Reorder the terms: -84 + -19s + -1s2 = 19s + -19s + s2 + -1s2 Combine like terms: 19s + -19s = 0 -84 + -19s + -1s2 = 0 + s2 + -1s2 -84 + -19s + -1s2 = s2 + -1s2 Combine like terms: s2 + -1s2 = 0 -84 + -19s + -1s2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(84 + 19s + s2) = 0 Factor a trinomial. -1((12 + s)(7 + s)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + s)' equal to zero and attempt to solve: Simplifying 12 + s = 0 Solving 12 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + s = 0 + -12 Combine like terms: 12 + -12 = 0 0 + s = 0 + -12 s = 0 + -12 Combine like terms: 0 + -12 = -12 s = -12 Simplifying s = -12Subproblem 2
Set the factor '(7 + s)' equal to zero and attempt to solve: Simplifying 7 + s = 0 Solving 7 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + s = 0 + -7 Combine like terms: 7 + -7 = 0 0 + s = 0 + -7 s = 0 + -7 Combine like terms: 0 + -7 = -7 s = -7 Simplifying s = -7Solution
s = {-12, -7}
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