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Simplifying 2s2 + -38s + 48 = 0 Reorder the terms: 48 + -38s + 2s2 = 0 Solving 48 + -38s + 2s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -19s + s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -19s + s2)' equal to zero and attempt to solve: Simplifying 24 + -19s + s2 = 0 Solving 24 + -19s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -19s + -24 + s2 = 0 + -24 Reorder the terms: 24 + -24 + -19s + s2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -19s + s2 = 0 + -24 -19s + s2 = 0 + -24 Combine like terms: 0 + -24 = -24 -19s + s2 = -24 The s term is -19s. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19s + 90.25 + s2 = -24 + 90.25 Reorder the terms: 90.25 + -19s + s2 = -24 + 90.25 Combine like terms: -24 + 90.25 = 66.25 90.25 + -19s + s2 = 66.25 Factor a perfect square on the left side: (s + -9.5)(s + -9.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (s + -9.5) equal to 8.139410298 and -8.139410298.Subproblem 1
s + -9.5 = 8.139410298 Simplifying s + -9.5 = 8.139410298 Reorder the terms: -9.5 + s = 8.139410298 Solving -9.5 + s = 8.139410298 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + s = 8.139410298 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + s = 8.139410298 + 9.5 s = 8.139410298 + 9.5 Combine like terms: 8.139410298 + 9.5 = 17.639410298 s = 17.639410298 Simplifying s = 17.639410298Subproblem 2
s + -9.5 = -8.139410298 Simplifying s + -9.5 = -8.139410298 Reorder the terms: -9.5 + s = -8.139410298 Solving -9.5 + s = -8.139410298 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + s = -8.139410298 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + s = -8.139410298 + 9.5 s = -8.139410298 + 9.5 Combine like terms: -8.139410298 + 9.5 = 1.360589702 s = 1.360589702 Simplifying s = 1.360589702Solution
The solution to the problem is based on the solutions from the subproblems. s = {17.639410298, 1.360589702}Solution
s = {17.639410298, 1.360589702}
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