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Simplifying -8s2 + 2s + 4 = 0 Reorder the terms: 4 + 2s + -8s2 = 0 Solving 4 + 2s + -8s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + s + -4s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + s + -4s2)' equal to zero and attempt to solve: Simplifying 2 + s + -4s2 = 0 Solving 2 + s + -4s2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + -0.25s + s2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.25s + 0.5 + s2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.25s + s2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.25s + s2 = 0 + 0.5 -0.25s + s2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.25s + s2 = 0.5 The s term is s. 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. -0.25s + 0.25 + s2 = 0.5 + 0.25 Reorder the terms: 0.25 + -0.25s + s2 = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 0.25 + -0.25s + s2 = 0.75 Factor a perfect square on the left side: (s + 0.5)(s + 0.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (s + 0.5) equal to 0.866025404 and -0.866025404.Subproblem 1
s + 0.5 = 0.866025404 Simplifying s + 0.5 = 0.866025404 Reorder the terms: 0.5 + s = 0.866025404 Solving 0.5 + s = 0.866025404 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 = 0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + s = 0.866025404 + -0.5 s = 0.866025404 + -0.5 Combine like terms: 0.866025404 + -0.5 = 0.366025404 s = 0.366025404 Simplifying s = 0.366025404Subproblem 2
s + 0.5 = -0.866025404 Simplifying s + 0.5 = -0.866025404 Reorder the terms: 0.5 + s = -0.866025404 Solving 0.5 + s = -0.866025404 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 = -0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + s = -0.866025404 + -0.5 s = -0.866025404 + -0.5 Combine like terms: -0.866025404 + -0.5 = -1.366025404 s = -1.366025404 Simplifying s = -1.366025404Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.366025404, -1.366025404}Solution
s = {0.366025404, -1.366025404}
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