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Simplifying s2 + 22s = 27 Reorder the terms: 22s + s2 = 27 Solving 22s + s2 = 27 Solving for variable 's'. Reorder the terms: -27 + 22s + s2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 22s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 22s + 27 + s2 = 0 + 27 Reorder the terms: -27 + 27 + 22s + s2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 22s + s2 = 0 + 27 22s + s2 = 0 + 27 Combine like terms: 0 + 27 = 27 22s + s2 = 27 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 = 27 + 121 Reorder the terms: 121 + 22s + s2 = 27 + 121 Combine like terms: 27 + 121 = 148 121 + 22s + s2 = 148 Factor a perfect square on the left side: (s + 11)(s + 11) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (s + 11) equal to 12.165525061 and -12.165525061.Subproblem 1
s + 11 = 12.165525061 Simplifying s + 11 = 12.165525061 Reorder the terms: 11 + s = 12.165525061 Solving 11 + s = 12.165525061 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 = 12.165525061 + -11 Combine like terms: 11 + -11 = 0 0 + s = 12.165525061 + -11 s = 12.165525061 + -11 Combine like terms: 12.165525061 + -11 = 1.165525061 s = 1.165525061 Simplifying s = 1.165525061Subproblem 2
s + 11 = -12.165525061 Simplifying s + 11 = -12.165525061 Reorder the terms: 11 + s = -12.165525061 Solving 11 + s = -12.165525061 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 = -12.165525061 + -11 Combine like terms: 11 + -11 = 0 0 + s = -12.165525061 + -11 s = -12.165525061 + -11 Combine like terms: -12.165525061 + -11 = -23.165525061 s = -23.165525061 Simplifying s = -23.165525061Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.165525061, -23.165525061}
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