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Simplifying 4s3 + 8s2 + -24s = 0 Reorder the terms: -24s + 8s2 + 4s3 = 0 Solving -24s + 8s2 + 4s3 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '4s'. 4s(-6 + 2s + s2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing s to the left, all other terms to the right. Simplifying s = 0Subproblem 2
Set the factor '(-6 + 2s + s2)' equal to zero and attempt to solve: Simplifying -6 + 2s + s2 = 0 Solving -6 + 2s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2s + 6 + s2 = 0 + 6 Reorder the terms: -6 + 6 + 2s + s2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2s + s2 = 0 + 6 2s + s2 = 0 + 6 Combine like terms: 0 + 6 = 6 2s + s2 = 6 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 6 + 1 Reorder the terms: 1 + 2s + s2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2s + s2 = 7 Factor a perfect square on the left side: (s + 1)(s + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (s + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
s + 1 = 2.645751311 Simplifying s + 1 = 2.645751311 Reorder the terms: 1 + s = 2.645751311 Solving 1 + s = 2.645751311 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + s = 2.645751311 + -1 s = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 s = 1.645751311 Simplifying s = 1.645751311Subproblem 2
s + 1 = -2.645751311 Simplifying s + 1 = -2.645751311 Reorder the terms: 1 + s = -2.645751311 Solving 1 + s = -2.645751311 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + s = -2.645751311 + -1 s = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 s = -3.645751311 Simplifying s = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.645751311, -3.645751311}Solution
s = {0, 1.645751311, -3.645751311}
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