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Simplifying (s * s) + (s + 1)(s + 1) + (s + 2)(s + 2) = 365 Multiply s * s (s2) + (s + 1)(s + 1) + (s + 2)(s + 2) = 365 s2 + (s + 1)(s + 1) + (s + 2)(s + 2) = 365 Reorder the terms: s2 + (1 + s)(s + 1) + (s + 2)(s + 2) = 365 Reorder the terms: s2 + (1 + s)(1 + s) + (s + 2)(s + 2) = 365 Multiply (1 + s) * (1 + s) s2 + (1(1 + s) + s(1 + s)) + (s + 2)(s + 2) = 365 s2 + ((1 * 1 + s * 1) + s(1 + s)) + (s + 2)(s + 2) = 365 s2 + ((1 + 1s) + s(1 + s)) + (s + 2)(s + 2) = 365 s2 + (1 + 1s + (1 * s + s * s)) + (s + 2)(s + 2) = 365 s2 + (1 + 1s + (1s + s2)) + (s + 2)(s + 2) = 365 Combine like terms: 1s + 1s = 2s s2 + (1 + 2s + s2) + (s + 2)(s + 2) = 365 Reorder the terms: s2 + 1 + 2s + s2 + (2 + s)(s + 2) = 365 Reorder the terms: s2 + 1 + 2s + s2 + (2 + s)(2 + s) = 365 Multiply (2 + s) * (2 + s) s2 + 1 + 2s + s2 + (2(2 + s) + s(2 + s)) = 365 s2 + 1 + 2s + s2 + ((2 * 2 + s * 2) + s(2 + s)) = 365 s2 + 1 + 2s + s2 + ((4 + 2s) + s(2 + s)) = 365 s2 + 1 + 2s + s2 + (4 + 2s + (2 * s + s * s)) = 365 s2 + 1 + 2s + s2 + (4 + 2s + (2s + s2)) = 365 Combine like terms: 2s + 2s = 4s s2 + 1 + 2s + s2 + (4 + 4s + s2) = 365 Reorder the terms: 1 + 4 + 2s + 4s + s2 + s2 + s2 = 365 Combine like terms: 1 + 4 = 5 5 + 2s + 4s + s2 + s2 + s2 = 365 Combine like terms: 2s + 4s = 6s 5 + 6s + s2 + s2 + s2 = 365 Combine like terms: s2 + s2 = 2s2 5 + 6s + 2s2 + s2 = 365 Combine like terms: 2s2 + s2 = 3s2 5 + 6s + 3s2 = 365 Solving 5 + 6s + 3s2 = 365 Solving for variable 's'. Reorder the terms: 5 + -365 + 6s + 3s2 = 365 + -365 Combine like terms: 5 + -365 = -360 -360 + 6s + 3s2 = 365 + -365 Combine like terms: 365 + -365 = 0 -360 + 6s + 3s2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-120 + 2s + s2) = 0 Factor a trinomial. 3((-12 + -1s)(10 + -1s)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + -1s)' equal to zero and attempt to solve: Simplifying -12 + -1s = 0 Solving -12 + -1s = 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 + -1s = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1s = 0 + 12 -1s = 0 + 12 Combine like terms: 0 + 12 = 12 -1s = 12 Divide each side by '-1'. s = -12 Simplifying s = -12Subproblem 2
Set the factor '(10 + -1s)' equal to zero and attempt to solve: Simplifying 10 + -1s = 0 Solving 10 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1s = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1s = 0 + -10 -1s = 0 + -10 Combine like terms: 0 + -10 = -10 -1s = -10 Divide each side by '-1'. s = 10 Simplifying s = 10Solution
s = {-12, 10}
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