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Simplifying 2s3 + 3s2 + -3s = 0 Reorder the terms: -3s + 3s2 + 2s3 = 0 Solving -3s + 3s2 + 2s3 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), 's'. s(-3 + 3s + 2s2) = 0Subproblem 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 '(-3 + 3s + 2s2)' equal to zero and attempt to solve: Simplifying -3 + 3s + 2s2 = 0 Solving -3 + 3s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 1.5s + s2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.5s + 1.5 + s2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.5s + s2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.5s + s2 = 0 + 1.5 1.5s + s2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.5s + s2 = 1.5 The s term is 1.5s. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5s + 0.5625 + s2 = 1.5 + 0.5625 Reorder the terms: 0.5625 + 1.5s + s2 = 1.5 + 0.5625 Combine like terms: 1.5 + 0.5625 = 2.0625 0.5625 + 1.5s + s2 = 2.0625 Factor a perfect square on the left side: (s + 0.75)(s + 0.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (s + 0.75) equal to 1.436140662 and -1.436140662.Subproblem 1
s + 0.75 = 1.436140662 Simplifying s + 0.75 = 1.436140662 Reorder the terms: 0.75 + s = 1.436140662 Solving 0.75 + s = 1.436140662 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = 1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = 1.436140662 + -0.75 s = 1.436140662 + -0.75 Combine like terms: 1.436140662 + -0.75 = 0.686140662 s = 0.686140662 Simplifying s = 0.686140662Subproblem 2
s + 0.75 = -1.436140662 Simplifying s + 0.75 = -1.436140662 Reorder the terms: 0.75 + s = -1.436140662 Solving 0.75 + s = -1.436140662 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = -1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = -1.436140662 + -0.75 s = -1.436140662 + -0.75 Combine like terms: -1.436140662 + -0.75 = -2.186140662 s = -2.186140662 Simplifying s = -2.186140662Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.686140662, -2.186140662}Solution
s = {0, 0.686140662, -2.186140662}
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