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Simplifying 63 = (5 + s)(7 + s) Multiply (5 + s) * (7 + s) 63 = (5(7 + s) + s(7 + s)) 63 = ((7 * 5 + s * 5) + s(7 + s)) 63 = ((35 + 5s) + s(7 + s)) 63 = (35 + 5s + (7 * s + s * s)) 63 = (35 + 5s + (7s + s2)) Combine like terms: 5s + 7s = 12s 63 = (35 + 12s + s2) Solving 63 = 35 + 12s + s2 Solving for variable 's'. Combine like terms: 63 + -35 = 28 28 + -12s + -1s2 = 35 + 12s + s2 + -35 + -12s + -1s2 Reorder the terms: 28 + -12s + -1s2 = 35 + -35 + 12s + -12s + s2 + -1s2 Combine like terms: 35 + -35 = 0 28 + -12s + -1s2 = 0 + 12s + -12s + s2 + -1s2 28 + -12s + -1s2 = 12s + -12s + s2 + -1s2 Combine like terms: 12s + -12s = 0 28 + -12s + -1s2 = 0 + s2 + -1s2 28 + -12s + -1s2 = s2 + -1s2 Combine like terms: s2 + -1s2 = 0 28 + -12s + -1s2 = 0 Factor a trinomial. (2 + -1s)(14 + s) = 0Subproblem 1
Set the factor '(2 + -1s)' equal to zero and attempt to solve: Simplifying 2 + -1s = 0 Solving 2 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1s = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1s = 0 + -2 -1s = 0 + -2 Combine like terms: 0 + -2 = -2 -1s = -2 Divide each side by '-1'. s = 2 Simplifying s = 2Subproblem 2
Set the factor '(14 + s)' equal to zero and attempt to solve: Simplifying 14 + s = 0 Solving 14 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + s = 0 + -14 Combine like terms: 14 + -14 = 0 0 + s = 0 + -14 s = 0 + -14 Combine like terms: 0 + -14 = -14 s = -14 Simplifying s = -14Solution
s = {2, -14}
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