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Simplifying s2 + -32 = 2 + 12s Reorder the terms: -32 + s2 = 2 + 12s Solving -32 + s2 = 2 + 12s Solving for variable 's'. Reorder the terms: -32 + -2 + -12s + s2 = 2 + 12s + -2 + -12s Combine like terms: -32 + -2 = -34 -34 + -12s + s2 = 2 + 12s + -2 + -12s Reorder the terms: -34 + -12s + s2 = 2 + -2 + 12s + -12s Combine like terms: 2 + -2 = 0 -34 + -12s + s2 = 0 + 12s + -12s -34 + -12s + s2 = 12s + -12s Combine like terms: 12s + -12s = 0 -34 + -12s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -12s + 34 + s2 = 0 + 34 Reorder the terms: -34 + 34 + -12s + s2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -12s + s2 = 0 + 34 -12s + s2 = 0 + 34 Combine like terms: 0 + 34 = 34 -12s + s2 = 34 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 = 34 + 36 Reorder the terms: 36 + -12s + s2 = 34 + 36 Combine like terms: 34 + 36 = 70 36 + -12s + s2 = 70 Factor a perfect square on the left side: (s + -6)(s + -6) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (s + -6) equal to 8.366600265 and -8.366600265.Subproblem 1
s + -6 = 8.366600265 Simplifying s + -6 = 8.366600265 Reorder the terms: -6 + s = 8.366600265 Solving -6 + s = 8.366600265 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 = 8.366600265 + 6 Combine like terms: -6 + 6 = 0 0 + s = 8.366600265 + 6 s = 8.366600265 + 6 Combine like terms: 8.366600265 + 6 = 14.366600265 s = 14.366600265 Simplifying s = 14.366600265Subproblem 2
s + -6 = -8.366600265 Simplifying s + -6 = -8.366600265 Reorder the terms: -6 + s = -8.366600265 Solving -6 + s = -8.366600265 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 = -8.366600265 + 6 Combine like terms: -6 + 6 = 0 0 + s = -8.366600265 + 6 s = -8.366600265 + 6 Combine like terms: -8.366600265 + 6 = -2.366600265 s = -2.366600265 Simplifying s = -2.366600265Solution
The solution to the problem is based on the solutions from the subproblems. s = {14.366600265, -2.366600265}
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