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Simplifying 6(13 + -1s) * 4s = 62 Reorder the terms for easier multiplication: 6 * 4s(13 + -1s) = 62 Multiply 6 * 4 24s(13 + -1s) = 62 (13 * 24s + -1s * 24s) = 62 (312s + -24s2) = 62 Solving 312s + -24s2 = 62 Solving for variable 's'. Reorder the terms: -62 + 312s + -24s2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + 312s + -24s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + 156s + -12s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + 156s + -12s2)' equal to zero and attempt to solve: Simplifying -31 + 156s + -12s2 = 0 Solving -31 + 156s + -12s2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 2.583333333 + -13s + s2 = 0 Move the constant term to the right: Add '-2.583333333' to each side of the equation. 2.583333333 + -13s + -2.583333333 + s2 = 0 + -2.583333333 Reorder the terms: 2.583333333 + -2.583333333 + -13s + s2 = 0 + -2.583333333 Combine like terms: 2.583333333 + -2.583333333 = 0.000000000 0.000000000 + -13s + s2 = 0 + -2.583333333 -13s + s2 = 0 + -2.583333333 Combine like terms: 0 + -2.583333333 = -2.583333333 -13s + s2 = -2.583333333 The s term is -13s. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13s + 42.25 + s2 = -2.583333333 + 42.25 Reorder the terms: 42.25 + -13s + s2 = -2.583333333 + 42.25 Combine like terms: -2.583333333 + 42.25 = 39.666666667 42.25 + -13s + s2 = 39.666666667 Factor a perfect square on the left side: (s + -6.5)(s + -6.5) = 39.666666667 Calculate the square root of the right side: 6.298147876 Break this problem into two subproblems by setting (s + -6.5) equal to 6.298147876 and -6.298147876.Subproblem 1
s + -6.5 = 6.298147876 Simplifying s + -6.5 = 6.298147876 Reorder the terms: -6.5 + s = 6.298147876 Solving -6.5 + s = 6.298147876 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + s = 6.298147876 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + s = 6.298147876 + 6.5 s = 6.298147876 + 6.5 Combine like terms: 6.298147876 + 6.5 = 12.798147876 s = 12.798147876 Simplifying s = 12.798147876Subproblem 2
s + -6.5 = -6.298147876 Simplifying s + -6.5 = -6.298147876 Reorder the terms: -6.5 + s = -6.298147876 Solving -6.5 + s = -6.298147876 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + s = -6.298147876 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + s = -6.298147876 + 6.5 s = -6.298147876 + 6.5 Combine like terms: -6.298147876 + 6.5 = 0.201852124 s = 0.201852124 Simplifying s = 0.201852124Solution
The solution to the problem is based on the solutions from the subproblems. s = {12.798147876, 0.201852124}Solution
s = {12.798147876, 0.201852124}
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