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Simplifying s2 + 10s + 1 = 0 Reorder the terms: 1 + 10s + s2 = 0 Solving 1 + 10s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 10s + -1 + s2 = 0 + -1 Reorder the terms: 1 + -1 + 10s + s2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10s + s2 = 0 + -1 10s + s2 = 0 + -1 Combine like terms: 0 + -1 = -1 10s + s2 = -1 The s term is 10s. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10s + 25 + s2 = -1 + 25 Reorder the terms: 25 + 10s + s2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + 10s + s2 = 24 Factor a perfect square on the left side: (s + 5)(s + 5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (s + 5) equal to 4.898979486 and -4.898979486.Subproblem 1
s + 5 = 4.898979486 Simplifying s + 5 = 4.898979486 Reorder the terms: 5 + s = 4.898979486 Solving 5 + s = 4.898979486 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = 4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + s = 4.898979486 + -5 s = 4.898979486 + -5 Combine like terms: 4.898979486 + -5 = -0.101020514 s = -0.101020514 Simplifying s = -0.101020514Subproblem 2
s + 5 = -4.898979486 Simplifying s + 5 = -4.898979486 Reorder the terms: 5 + s = -4.898979486 Solving 5 + s = -4.898979486 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = -4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + s = -4.898979486 + -5 s = -4.898979486 + -5 Combine like terms: -4.898979486 + -5 = -9.898979486 s = -9.898979486 Simplifying s = -9.898979486Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.101020514, -9.898979486}
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