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Simplifying s2 + -26s = 11 Reorder the terms: -26s + s2 = 11 Solving -26s + s2 = 11 Solving for variable 's'. Reorder the terms: -11 + -26s + s2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -26s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -26s + 11 + s2 = 0 + 11 Reorder the terms: -11 + 11 + -26s + s2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -26s + s2 = 0 + 11 -26s + s2 = 0 + 11 Combine like terms: 0 + 11 = 11 -26s + s2 = 11 The s term is -26s. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26s + 169 + s2 = 11 + 169 Reorder the terms: 169 + -26s + s2 = 11 + 169 Combine like terms: 11 + 169 = 180 169 + -26s + s2 = 180 Factor a perfect square on the left side: (s + -13)(s + -13) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (s + -13) equal to 13.416407865 and -13.416407865.Subproblem 1
s + -13 = 13.416407865 Simplifying s + -13 = 13.416407865 Reorder the terms: -13 + s = 13.416407865 Solving -13 + s = 13.416407865 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + s = 13.416407865 + 13 Combine like terms: -13 + 13 = 0 0 + s = 13.416407865 + 13 s = 13.416407865 + 13 Combine like terms: 13.416407865 + 13 = 26.416407865 s = 26.416407865 Simplifying s = 26.416407865Subproblem 2
s + -13 = -13.416407865 Simplifying s + -13 = -13.416407865 Reorder the terms: -13 + s = -13.416407865 Solving -13 + s = -13.416407865 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + s = -13.416407865 + 13 Combine like terms: -13 + 13 = 0 0 + s = -13.416407865 + 13 s = -13.416407865 + 13 Combine like terms: -13.416407865 + 13 = -0.416407865 s = -0.416407865 Simplifying s = -0.416407865Solution
The solution to the problem is based on the solutions from the subproblems. s = {26.416407865, -0.416407865}
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