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Simplifying 8s2 + -159s + 758 = 0 Reorder the terms: 758 + -159s + 8s2 = 0 Solving 758 + -159s + 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'. 94.75 + -19.875s + s2 = 0 Move the constant term to the right: Add '-94.75' to each side of the equation. 94.75 + -19.875s + -94.75 + s2 = 0 + -94.75 Reorder the terms: 94.75 + -94.75 + -19.875s + s2 = 0 + -94.75 Combine like terms: 94.75 + -94.75 = 0.00 0.00 + -19.875s + s2 = 0 + -94.75 -19.875s + s2 = 0 + -94.75 Combine like terms: 0 + -94.75 = -94.75 -19.875s + s2 = -94.75 The s term is -19.875s. Take half its coefficient (-9.9375). Square it (98.75390625) and add it to both sides. Add '98.75390625' to each side of the equation. -19.875s + 98.75390625 + s2 = -94.75 + 98.75390625 Reorder the terms: 98.75390625 + -19.875s + s2 = -94.75 + 98.75390625 Combine like terms: -94.75 + 98.75390625 = 4.00390625 98.75390625 + -19.875s + s2 = 4.00390625 Factor a perfect square on the left side: (s + -9.9375)(s + -9.9375) = 4.00390625 Calculate the square root of the right side: 2.000976324 Break this problem into two subproblems by setting (s + -9.9375) equal to 2.000976324 and -2.000976324.Subproblem 1
s + -9.9375 = 2.000976324 Simplifying s + -9.9375 = 2.000976324 Reorder the terms: -9.9375 + s = 2.000976324 Solving -9.9375 + s = 2.000976324 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '9.9375' to each side of the equation. -9.9375 + 9.9375 + s = 2.000976324 + 9.9375 Combine like terms: -9.9375 + 9.9375 = 0.0000 0.0000 + s = 2.000976324 + 9.9375 s = 2.000976324 + 9.9375 Combine like terms: 2.000976324 + 9.9375 = 11.938476324 s = 11.938476324 Simplifying s = 11.938476324Subproblem 2
s + -9.9375 = -2.000976324 Simplifying s + -9.9375 = -2.000976324 Reorder the terms: -9.9375 + s = -2.000976324 Solving -9.9375 + s = -2.000976324 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '9.9375' to each side of the equation. -9.9375 + 9.9375 + s = -2.000976324 + 9.9375 Combine like terms: -9.9375 + 9.9375 = 0.0000 0.0000 + s = -2.000976324 + 9.9375 s = -2.000976324 + 9.9375 Combine like terms: -2.000976324 + 9.9375 = 7.936523676 s = 7.936523676 Simplifying s = 7.936523676Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.938476324, 7.936523676}
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