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Simplifying s2 + -26s = 23 Reorder the terms: -26s + s2 = 23 Solving -26s + s2 = 23 Solving for variable 's'. Reorder the terms: -23 + -26s + s2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -26s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -26s + 23 + s2 = 0 + 23 Reorder the terms: -23 + 23 + -26s + s2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -26s + s2 = 0 + 23 -26s + s2 = 0 + 23 Combine like terms: 0 + 23 = 23 -26s + s2 = 23 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 = 23 + 169 Reorder the terms: 169 + -26s + s2 = 23 + 169 Combine like terms: 23 + 169 = 192 169 + -26s + s2 = 192 Factor a perfect square on the left side: (s + -13)(s + -13) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (s + -13) equal to 13.856406461 and -13.856406461.Subproblem 1
s + -13 = 13.856406461 Simplifying s + -13 = 13.856406461 Reorder the terms: -13 + s = 13.856406461 Solving -13 + s = 13.856406461 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 = 13.856406461 + 13 Combine like terms: -13 + 13 = 0 0 + s = 13.856406461 + 13 s = 13.856406461 + 13 Combine like terms: 13.856406461 + 13 = 26.856406461 s = 26.856406461 Simplifying s = 26.856406461Subproblem 2
s + -13 = -13.856406461 Simplifying s + -13 = -13.856406461 Reorder the terms: -13 + s = -13.856406461 Solving -13 + s = -13.856406461 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 = -13.856406461 + 13 Combine like terms: -13 + 13 = 0 0 + s = -13.856406461 + 13 s = -13.856406461 + 13 Combine like terms: -13.856406461 + 13 = -0.856406461 s = -0.856406461 Simplifying s = -0.856406461Solution
The solution to the problem is based on the solutions from the subproblems. s = {26.856406461, -0.856406461}
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