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Simplifying -2s2 + -56s + 6 = 0 Reorder the terms: 6 + -56s + -2s2 = 0 Solving 6 + -56s + -2s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -28s + -1s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -28s + -1s2)' equal to zero and attempt to solve: Simplifying 3 + -28s + -1s2 = 0 Solving 3 + -28s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 28s + s2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 28s + 3 + s2 = 0 + 3 Reorder the terms: -3 + 3 + 28s + s2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 28s + s2 = 0 + 3 28s + s2 = 0 + 3 Combine like terms: 0 + 3 = 3 28s + s2 = 3 The s term is 28s. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28s + 196 + s2 = 3 + 196 Reorder the terms: 196 + 28s + s2 = 3 + 196 Combine like terms: 3 + 196 = 199 196 + 28s + s2 = 199 Factor a perfect square on the left side: (s + 14)(s + 14) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (s + 14) equal to 14.10673598 and -14.10673598.Subproblem 1
s + 14 = 14.10673598 Simplifying s + 14 = 14.10673598 Reorder the terms: 14 + s = 14.10673598 Solving 14 + s = 14.10673598 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + s = 14.10673598 + -14 Combine like terms: 14 + -14 = 0 0 + s = 14.10673598 + -14 s = 14.10673598 + -14 Combine like terms: 14.10673598 + -14 = 0.10673598 s = 0.10673598 Simplifying s = 0.10673598Subproblem 2
s + 14 = -14.10673598 Simplifying s + 14 = -14.10673598 Reorder the terms: 14 + s = -14.10673598 Solving 14 + s = -14.10673598 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + s = -14.10673598 + -14 Combine like terms: 14 + -14 = 0 0 + s = -14.10673598 + -14 s = -14.10673598 + -14 Combine like terms: -14.10673598 + -14 = -28.10673598 s = -28.10673598 Simplifying s = -28.10673598Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.10673598, -28.10673598}Solution
s = {0.10673598, -28.10673598}
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