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Simplifying s2 + 18s + -37 = 4 Reorder the terms: -37 + 18s + s2 = 4 Solving -37 + 18s + s2 = 4 Solving for variable 's'. Reorder the terms: -37 + -4 + 18s + s2 = 4 + -4 Combine like terms: -37 + -4 = -41 -41 + 18s + s2 = 4 + -4 Combine like terms: 4 + -4 = 0 -41 + 18s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 18s + 41 + s2 = 0 + 41 Reorder the terms: -41 + 41 + 18s + s2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 18s + s2 = 0 + 41 18s + s2 = 0 + 41 Combine like terms: 0 + 41 = 41 18s + s2 = 41 The s term is 18s. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18s + 81 + s2 = 41 + 81 Reorder the terms: 81 + 18s + s2 = 41 + 81 Combine like terms: 41 + 81 = 122 81 + 18s + s2 = 122 Factor a perfect square on the left side: (s + 9)(s + 9) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (s + 9) equal to 11.045361017 and -11.045361017.Subproblem 1
s + 9 = 11.045361017 Simplifying s + 9 = 11.045361017 Reorder the terms: 9 + s = 11.045361017 Solving 9 + s = 11.045361017 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = 11.045361017 + -9 Combine like terms: 9 + -9 = 0 0 + s = 11.045361017 + -9 s = 11.045361017 + -9 Combine like terms: 11.045361017 + -9 = 2.045361017 s = 2.045361017 Simplifying s = 2.045361017Subproblem 2
s + 9 = -11.045361017 Simplifying s + 9 = -11.045361017 Reorder the terms: 9 + s = -11.045361017 Solving 9 + s = -11.045361017 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = -11.045361017 + -9 Combine like terms: 9 + -9 = 0 0 + s = -11.045361017 + -9 s = -11.045361017 + -9 Combine like terms: -11.045361017 + -9 = -20.045361017 s = -20.045361017 Simplifying s = -20.045361017Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.045361017, -20.045361017}
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