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Simplifying -5s2 + 5s + 9 = 0 Reorder the terms: 9 + 5s + -5s2 = 0 Solving 9 + 5s + -5s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + -1s + s2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1s + 1.8 + s2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1s + s2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1s + s2 = 0 + 1.8 -1s + s2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1s + s2 = 1.8 The s term is -1s. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1s + 0.25 + s2 = 1.8 + 0.25 Reorder the terms: 0.25 + -1s + s2 = 1.8 + 0.25 Combine like terms: 1.8 + 0.25 = 2.05 0.25 + -1s + s2 = 2.05 Factor a perfect square on the left side: (s + -0.5)(s + -0.5) = 2.05 Calculate the square root of the right side: 1.431782106 Break this problem into two subproblems by setting (s + -0.5) equal to 1.431782106 and -1.431782106.Subproblem 1
s + -0.5 = 1.431782106 Simplifying s + -0.5 = 1.431782106 Reorder the terms: -0.5 + s = 1.431782106 Solving -0.5 + s = 1.431782106 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = 1.431782106 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = 1.431782106 + 0.5 s = 1.431782106 + 0.5 Combine like terms: 1.431782106 + 0.5 = 1.931782106 s = 1.931782106 Simplifying s = 1.931782106Subproblem 2
s + -0.5 = -1.431782106 Simplifying s + -0.5 = -1.431782106 Reorder the terms: -0.5 + s = -1.431782106 Solving -0.5 + s = -1.431782106 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = -1.431782106 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = -1.431782106 + 0.5 s = -1.431782106 + 0.5 Combine like terms: -1.431782106 + 0.5 = -0.931782106 s = -0.931782106 Simplifying s = -0.931782106Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.931782106, -0.931782106}
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