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Simplifying s2 + -22s = 37 Reorder the terms: -22s + s2 = 37 Solving -22s + s2 = 37 Solving for variable 's'. Reorder the terms: -37 + -22s + s2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -22s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -22s + 37 + s2 = 0 + 37 Reorder the terms: -37 + 37 + -22s + s2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -22s + s2 = 0 + 37 -22s + s2 = 0 + 37 Combine like terms: 0 + 37 = 37 -22s + s2 = 37 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 = 37 + 121 Reorder the terms: 121 + -22s + s2 = 37 + 121 Combine like terms: 37 + 121 = 158 121 + -22s + s2 = 158 Factor a perfect square on the left side: (s + -11)(s + -11) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (s + -11) equal to 12.56980509 and -12.56980509.Subproblem 1
s + -11 = 12.56980509 Simplifying s + -11 = 12.56980509 Reorder the terms: -11 + s = 12.56980509 Solving -11 + s = 12.56980509 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 = 12.56980509 + 11 Combine like terms: -11 + 11 = 0 0 + s = 12.56980509 + 11 s = 12.56980509 + 11 Combine like terms: 12.56980509 + 11 = 23.56980509 s = 23.56980509 Simplifying s = 23.56980509Subproblem 2
s + -11 = -12.56980509 Simplifying s + -11 = -12.56980509 Reorder the terms: -11 + s = -12.56980509 Solving -11 + s = -12.56980509 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 = -12.56980509 + 11 Combine like terms: -11 + 11 = 0 0 + s = -12.56980509 + 11 s = -12.56980509 + 11 Combine like terms: -12.56980509 + 11 = -1.56980509 s = -1.56980509 Simplifying s = -1.56980509Solution
The solution to the problem is based on the solutions from the subproblems. s = {23.56980509, -1.56980509}
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