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Simplifying s2 + 22s + -34 = 43 Reorder the terms: -34 + 22s + s2 = 43 Solving -34 + 22s + s2 = 43 Solving for variable 's'. Reorder the terms: -34 + -43 + 22s + s2 = 43 + -43 Combine like terms: -34 + -43 = -77 -77 + 22s + s2 = 43 + -43 Combine like terms: 43 + -43 = 0 -77 + 22s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 22s + 77 + s2 = 0 + 77 Reorder the terms: -77 + 77 + 22s + s2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 22s + s2 = 0 + 77 22s + s2 = 0 + 77 Combine like terms: 0 + 77 = 77 22s + s2 = 77 The s term is 22s. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22s + 121 + s2 = 77 + 121 Reorder the terms: 121 + 22s + s2 = 77 + 121 Combine like terms: 77 + 121 = 198 121 + 22s + s2 = 198 Factor a perfect square on the left side: (s + 11)(s + 11) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (s + 11) equal to 14.071247279 and -14.071247279.Subproblem 1
s + 11 = 14.071247279 Simplifying s + 11 = 14.071247279 Reorder the terms: 11 + s = 14.071247279 Solving 11 + s = 14.071247279 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + s = 14.071247279 + -11 Combine like terms: 11 + -11 = 0 0 + s = 14.071247279 + -11 s = 14.071247279 + -11 Combine like terms: 14.071247279 + -11 = 3.071247279 s = 3.071247279 Simplifying s = 3.071247279Subproblem 2
s + 11 = -14.071247279 Simplifying s + 11 = -14.071247279 Reorder the terms: 11 + s = -14.071247279 Solving 11 + s = -14.071247279 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + s = -14.071247279 + -11 Combine like terms: 11 + -11 = 0 0 + s = -14.071247279 + -11 s = -14.071247279 + -11 Combine like terms: -14.071247279 + -11 = -25.071247279 s = -25.071247279 Simplifying s = -25.071247279Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.071247279, -25.071247279}
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