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Simplifying 8s2 + -6s + -8 = 0 Reorder the terms: -8 + -6s + 8s2 = 0 Solving -8 + -6s + 8s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -3s + 4s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -3s + 4s2)' equal to zero and attempt to solve: Simplifying -4 + -3s + 4s2 = 0 Solving -4 + -3s + 4s2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -0.75s + s2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.75s + 1 + s2 = 0 + 1 Reorder the terms: -1 + 1 + -0.75s + s2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.75s + s2 = 0 + 1 -0.75s + s2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.75s + s2 = 1 The s term is -0.75s. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75s + 0.140625 + s2 = 1 + 0.140625 Reorder the terms: 0.140625 + -0.75s + s2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + -0.75s + s2 = 1.140625 Factor a perfect square on the left side: (s + -0.375)(s + -0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (s + -0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
s + -0.375 = 1.068000468 Simplifying s + -0.375 = 1.068000468 Reorder the terms: -0.375 + s = 1.068000468 Solving -0.375 + s = 1.068000468 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + s = 1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + s = 1.068000468 + 0.375 s = 1.068000468 + 0.375 Combine like terms: 1.068000468 + 0.375 = 1.443000468 s = 1.443000468 Simplifying s = 1.443000468Subproblem 2
s + -0.375 = -1.068000468 Simplifying s + -0.375 = -1.068000468 Reorder the terms: -0.375 + s = -1.068000468 Solving -0.375 + s = -1.068000468 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + s = -1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + s = -1.068000468 + 0.375 s = -1.068000468 + 0.375 Combine like terms: -1.068000468 + 0.375 = -0.693000468 s = -0.693000468 Simplifying s = -0.693000468Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.443000468, -0.693000468}Solution
s = {1.443000468, -0.693000468}
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