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Simplifying 8s2 + 9s + -5 = 0 Reorder the terms: -5 + 9s + 8s2 = 0 Solving -5 + 9s + 8s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 1.125s + s2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.125s + 0.625 + s2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.125s + s2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.125s + s2 = 0 + 0.625 1.125s + s2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.125s + s2 = 0.625 The s term is 1.125s. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125s + 0.31640625 + s2 = 0.625 + 0.31640625 Reorder the terms: 0.31640625 + 1.125s + s2 = 0.625 + 0.31640625 Combine like terms: 0.625 + 0.31640625 = 0.94140625 0.31640625 + 1.125s + s2 = 0.94140625 Factor a perfect square on the left side: (s + 0.5625)(s + 0.5625) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (s + 0.5625) equal to 0.970260919 and -0.970260919.Subproblem 1
s + 0.5625 = 0.970260919 Simplifying s + 0.5625 = 0.970260919 Reorder the terms: 0.5625 + s = 0.970260919 Solving 0.5625 + s = 0.970260919 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + s = 0.970260919 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + s = 0.970260919 + -0.5625 s = 0.970260919 + -0.5625 Combine like terms: 0.970260919 + -0.5625 = 0.407760919 s = 0.407760919 Simplifying s = 0.407760919Subproblem 2
s + 0.5625 = -0.970260919 Simplifying s + 0.5625 = -0.970260919 Reorder the terms: 0.5625 + s = -0.970260919 Solving 0.5625 + s = -0.970260919 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + s = -0.970260919 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + s = -0.970260919 + -0.5625 s = -0.970260919 + -0.5625 Combine like terms: -0.970260919 + -0.5625 = -1.532760919 s = -1.532760919 Simplifying s = -1.532760919Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.407760919, -1.532760919}
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