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Simplifying 8(9s2 + -108s + -14) = 0 Reorder the terms: 8(-14 + -108s + 9s2) = 0 (-14 * 8 + -108s * 8 + 9s2 * 8) = 0 (-112 + -864s + 72s2) = 0 Solving -112 + -864s + 72s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '8'. 8(-14 + -108s + 9s2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-14 + -108s + 9s2)' equal to zero and attempt to solve: Simplifying -14 + -108s + 9s2 = 0 Solving -14 + -108s + 9s2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + -12s + s2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -12s + 1.555555556 + s2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -12s + s2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -12s + s2 = 0 + 1.555555556 -12s + s2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -12s + s2 = 1.555555556 The s term is -12s. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12s + 36 + s2 = 1.555555556 + 36 Reorder the terms: 36 + -12s + s2 = 1.555555556 + 36 Combine like terms: 1.555555556 + 36 = 37.555555556 36 + -12s + s2 = 37.555555556 Factor a perfect square on the left side: (s + -6)(s + -6) = 37.555555556 Calculate the square root of the right side: 6.12825877 Break this problem into two subproblems by setting (s + -6) equal to 6.12825877 and -6.12825877.Subproblem 1
s + -6 = 6.12825877 Simplifying s + -6 = 6.12825877 Reorder the terms: -6 + s = 6.12825877 Solving -6 + s = 6.12825877 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = 6.12825877 + 6 Combine like terms: -6 + 6 = 0 0 + s = 6.12825877 + 6 s = 6.12825877 + 6 Combine like terms: 6.12825877 + 6 = 12.12825877 s = 12.12825877 Simplifying s = 12.12825877Subproblem 2
s + -6 = -6.12825877 Simplifying s + -6 = -6.12825877 Reorder the terms: -6 + s = -6.12825877 Solving -6 + s = -6.12825877 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = -6.12825877 + 6 Combine like terms: -6 + 6 = 0 0 + s = -6.12825877 + 6 s = -6.12825877 + 6 Combine like terms: -6.12825877 + 6 = -0.12825877 s = -0.12825877 Simplifying s = -0.12825877Solution
The solution to the problem is based on the solutions from the subproblems. s = {12.12825877, -0.12825877}Solution
s = {12.12825877, -0.12825877}
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