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Simplifying 2s2 + -26s + 169 = -3 + 169 Reorder the terms: 169 + -26s + 2s2 = -3 + 169 Combine like terms: -3 + 169 = 166 169 + -26s + 2s2 = 166 Solving 169 + -26s + 2s2 = 166 Solving for variable 's'. Reorder the terms: 169 + -166 + -26s + 2s2 = 166 + -166 Combine like terms: 169 + -166 = 3 3 + -26s + 2s2 = 166 + -166 Combine like terms: 166 + -166 = 0 3 + -26s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -13s + s2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -13s + -1.5 + s2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -13s + s2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -13s + s2 = 0 + -1.5 -13s + s2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -13s + s2 = -1.5 The s term is -13s. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13s + 42.25 + s2 = -1.5 + 42.25 Reorder the terms: 42.25 + -13s + s2 = -1.5 + 42.25 Combine like terms: -1.5 + 42.25 = 40.75 42.25 + -13s + s2 = 40.75 Factor a perfect square on the left side: (s + -6.5)(s + -6.5) = 40.75 Calculate the square root of the right side: 6.383572667 Break this problem into two subproblems by setting (s + -6.5) equal to 6.383572667 and -6.383572667.Subproblem 1
s + -6.5 = 6.383572667 Simplifying s + -6.5 = 6.383572667 Reorder the terms: -6.5 + s = 6.383572667 Solving -6.5 + s = 6.383572667 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + s = 6.383572667 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + s = 6.383572667 + 6.5 s = 6.383572667 + 6.5 Combine like terms: 6.383572667 + 6.5 = 12.883572667 s = 12.883572667 Simplifying s = 12.883572667Subproblem 2
s + -6.5 = -6.383572667 Simplifying s + -6.5 = -6.383572667 Reorder the terms: -6.5 + s = -6.383572667 Solving -6.5 + s = -6.383572667 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + s = -6.383572667 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + s = -6.383572667 + 6.5 s = -6.383572667 + 6.5 Combine like terms: -6.383572667 + 6.5 = 0.116427333 s = 0.116427333 Simplifying s = 0.116427333Solution
The solution to the problem is based on the solutions from the subproblems. s = {12.883572667, 0.116427333}
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