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Simplifying 6s3 + -14s2 + 4s = 2s Reorder the terms: 4s + -14s2 + 6s3 = 2s Solving 4s + -14s2 + 6s3 = 2s Solving for variable 's'. Reorder the terms: 4s + -2s + -14s2 + 6s3 = 2s + -2s Combine like terms: 4s + -2s = 2s 2s + -14s2 + 6s3 = 2s + -2s Combine like terms: 2s + -2s = 0 2s + -14s2 + 6s3 = 0 Factor out the Greatest Common Factor (GCF), '2s'. 2s(1 + -7s + 3s2) = 0 Ignore the factor 2.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 '(1 + -7s + 3s2)' equal to zero and attempt to solve: Simplifying 1 + -7s + 3s2 = 0 Solving 1 + -7s + 3s2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -2.333333333s + s2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -2.333333333s + -0.3333333333 + s2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -2.333333333s + s2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -2.333333333s + s2 = 0 + -0.3333333333 -2.333333333s + s2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -2.333333333s + s2 = -0.3333333333 The s term is -2.333333333s. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333s + 1.361111112 + s2 = -0.3333333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333s + s2 = -0.3333333333 + 1.361111112 Combine like terms: -0.3333333333 + 1.361111112 = 1.0277777787 1.361111112 + -2.333333333s + s2 = 1.0277777787 Factor a perfect square on the left side: (s + -1.166666667)(s + -1.166666667) = 1.0277777787 Calculate the square root of the right side: 1.013793756 Break this problem into two subproblems by setting (s + -1.166666667) equal to 1.013793756 and -1.013793756.Subproblem 1
s + -1.166666667 = 1.013793756 Simplifying s + -1.166666667 = 1.013793756 Reorder the terms: -1.166666667 + s = 1.013793756 Solving -1.166666667 + s = 1.013793756 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + s = 1.013793756 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + s = 1.013793756 + 1.166666667 s = 1.013793756 + 1.166666667 Combine like terms: 1.013793756 + 1.166666667 = 2.180460423 s = 2.180460423 Simplifying s = 2.180460423Subproblem 2
s + -1.166666667 = -1.013793756 Simplifying s + -1.166666667 = -1.013793756 Reorder the terms: -1.166666667 + s = -1.013793756 Solving -1.166666667 + s = -1.013793756 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + s = -1.013793756 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + s = -1.013793756 + 1.166666667 s = -1.013793756 + 1.166666667 Combine like terms: -1.013793756 + 1.166666667 = 0.152872911 s = 0.152872911 Simplifying s = 0.152872911Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.180460423, 0.152872911}Solution
s = {0, 2.180460423, 0.152872911}
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