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Simplifying s2 + 29s + 88 = 0 Reorder the terms: 88 + 29s + s2 = 0 Solving 88 + 29s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-88' to each side of the equation. 88 + 29s + -88 + s2 = 0 + -88 Reorder the terms: 88 + -88 + 29s + s2 = 0 + -88 Combine like terms: 88 + -88 = 0 0 + 29s + s2 = 0 + -88 29s + s2 = 0 + -88 Combine like terms: 0 + -88 = -88 29s + s2 = -88 The s term is 29s. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29s + 210.25 + s2 = -88 + 210.25 Reorder the terms: 210.25 + 29s + s2 = -88 + 210.25 Combine like terms: -88 + 210.25 = 122.25 210.25 + 29s + s2 = 122.25 Factor a perfect square on the left side: (s + 14.5)(s + 14.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (s + 14.5) equal to 11.056672194 and -11.056672194.Subproblem 1
s + 14.5 = 11.056672194 Simplifying s + 14.5 = 11.056672194 Reorder the terms: 14.5 + s = 11.056672194 Solving 14.5 + s = 11.056672194 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + s = 11.056672194 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + s = 11.056672194 + -14.5 s = 11.056672194 + -14.5 Combine like terms: 11.056672194 + -14.5 = -3.443327806 s = -3.443327806 Simplifying s = -3.443327806Subproblem 2
s + 14.5 = -11.056672194 Simplifying s + 14.5 = -11.056672194 Reorder the terms: 14.5 + s = -11.056672194 Solving 14.5 + s = -11.056672194 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + s = -11.056672194 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + s = -11.056672194 + -14.5 s = -11.056672194 + -14.5 Combine like terms: -11.056672194 + -14.5 = -25.556672194 s = -25.556672194 Simplifying s = -25.556672194Solution
The solution to the problem is based on the solutions from the subproblems. s = {-3.443327806, -25.556672194}
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