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Simplifying s2 + 20s + -17 = 0 Reorder the terms: -17 + 20s + s2 = 0 Solving -17 + 20s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 20s + 17 + s2 = 0 + 17 Reorder the terms: -17 + 17 + 20s + s2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 20s + s2 = 0 + 17 20s + s2 = 0 + 17 Combine like terms: 0 + 17 = 17 20s + s2 = 17 The s term is 20s. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20s + 100 + s2 = 17 + 100 Reorder the terms: 100 + 20s + s2 = 17 + 100 Combine like terms: 17 + 100 = 117 100 + 20s + s2 = 117 Factor a perfect square on the left side: (s + 10)(s + 10) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (s + 10) equal to 10.816653826 and -10.816653826.Subproblem 1
s + 10 = 10.816653826 Simplifying s + 10 = 10.816653826 Reorder the terms: 10 + s = 10.816653826 Solving 10 + s = 10.816653826 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + s = 10.816653826 + -10 Combine like terms: 10 + -10 = 0 0 + s = 10.816653826 + -10 s = 10.816653826 + -10 Combine like terms: 10.816653826 + -10 = 0.816653826 s = 0.816653826 Simplifying s = 0.816653826Subproblem 2
s + 10 = -10.816653826 Simplifying s + 10 = -10.816653826 Reorder the terms: 10 + s = -10.816653826 Solving 10 + s = -10.816653826 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + s = -10.816653826 + -10 Combine like terms: 10 + -10 = 0 0 + s = -10.816653826 + -10 s = -10.816653826 + -10 Combine like terms: -10.816653826 + -10 = -20.816653826 s = -20.816653826 Simplifying s = -20.816653826Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.816653826, -20.816653826}
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