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Simplifying 2s2 + 30s = -9 Reorder the terms: 30s + 2s2 = -9 Solving 30s + 2s2 = -9 Solving for variable 's'. Reorder the terms: 9 + 30s + 2s2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 30s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 15s + s2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 15s + -4.5 + s2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 15s + s2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 15s + s2 = 0 + -4.5 15s + s2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 15s + s2 = -4.5 The s term is 15s. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15s + 56.25 + s2 = -4.5 + 56.25 Reorder the terms: 56.25 + 15s + s2 = -4.5 + 56.25 Combine like terms: -4.5 + 56.25 = 51.75 56.25 + 15s + s2 = 51.75 Factor a perfect square on the left side: (s + 7.5)(s + 7.5) = 51.75 Calculate the square root of the right side: 7.193747285 Break this problem into two subproblems by setting (s + 7.5) equal to 7.193747285 and -7.193747285.Subproblem 1
s + 7.5 = 7.193747285 Simplifying s + 7.5 = 7.193747285 Reorder the terms: 7.5 + s = 7.193747285 Solving 7.5 + s = 7.193747285 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + s = 7.193747285 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + s = 7.193747285 + -7.5 s = 7.193747285 + -7.5 Combine like terms: 7.193747285 + -7.5 = -0.306252715 s = -0.306252715 Simplifying s = -0.306252715Subproblem 2
s + 7.5 = -7.193747285 Simplifying s + 7.5 = -7.193747285 Reorder the terms: 7.5 + s = -7.193747285 Solving 7.5 + s = -7.193747285 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + s = -7.193747285 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + s = -7.193747285 + -7.5 s = -7.193747285 + -7.5 Combine like terms: -7.193747285 + -7.5 = -14.693747285 s = -14.693747285 Simplifying s = -14.693747285Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.306252715, -14.693747285}
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