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Simplifying s2 + 9s = 18 Reorder the terms: 9s + s2 = 18 Solving 9s + s2 = 18 Solving for variable 's'. Reorder the terms: -18 + 9s + s2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 9s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 9s + 18 + s2 = 0 + 18 Reorder the terms: -18 + 18 + 9s + s2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 9s + s2 = 0 + 18 9s + s2 = 0 + 18 Combine like terms: 0 + 18 = 18 9s + s2 = 18 The s term is 9s. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9s + 20.25 + s2 = 18 + 20.25 Reorder the terms: 20.25 + 9s + s2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + 9s + s2 = 38.25 Factor a perfect square on the left side: (s + 4.5)(s + 4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (s + 4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
s + 4.5 = 6.184658438 Simplifying s + 4.5 = 6.184658438 Reorder the terms: 4.5 + s = 6.184658438 Solving 4.5 + s = 6.184658438 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + s = 6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + s = 6.184658438 + -4.5 s = 6.184658438 + -4.5 Combine like terms: 6.184658438 + -4.5 = 1.684658438 s = 1.684658438 Simplifying s = 1.684658438Subproblem 2
s + 4.5 = -6.184658438 Simplifying s + 4.5 = -6.184658438 Reorder the terms: 4.5 + s = -6.184658438 Solving 4.5 + s = -6.184658438 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + s = -6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + s = -6.184658438 + -4.5 s = -6.184658438 + -4.5 Combine like terms: -6.184658438 + -4.5 = -10.684658438 s = -10.684658438 Simplifying s = -10.684658438Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.684658438, -10.684658438}
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