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Simplifying s2 = 42 + -2s Solving s2 = 42 + -2s Solving for variable 's'. Reorder the terms: -42 + 2s + s2 = 42 + -2s + -42 + 2s Reorder the terms: -42 + 2s + s2 = 42 + -42 + -2s + 2s Combine like terms: 42 + -42 = 0 -42 + 2s + s2 = 0 + -2s + 2s -42 + 2s + s2 = -2s + 2s Combine like terms: -2s + 2s = 0 -42 + 2s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 2s + 42 + s2 = 0 + 42 Reorder the terms: -42 + 42 + 2s + s2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 2s + s2 = 0 + 42 2s + s2 = 0 + 42 Combine like terms: 0 + 42 = 42 2s + s2 = 42 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 42 + 1 Reorder the terms: 1 + 2s + s2 = 42 + 1 Combine like terms: 42 + 1 = 43 1 + 2s + s2 = 43 Factor a perfect square on the left side: (s + 1)(s + 1) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (s + 1) equal to 6.557438524 and -6.557438524.Subproblem 1
s + 1 = 6.557438524 Simplifying s + 1 = 6.557438524 Reorder the terms: 1 + s = 6.557438524 Solving 1 + s = 6.557438524 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 6.557438524 + -1 Combine like terms: 1 + -1 = 0 0 + s = 6.557438524 + -1 s = 6.557438524 + -1 Combine like terms: 6.557438524 + -1 = 5.557438524 s = 5.557438524 Simplifying s = 5.557438524Subproblem 2
s + 1 = -6.557438524 Simplifying s + 1 = -6.557438524 Reorder the terms: 1 + s = -6.557438524 Solving 1 + s = -6.557438524 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -6.557438524 + -1 Combine like terms: 1 + -1 = 0 0 + s = -6.557438524 + -1 s = -6.557438524 + -1 Combine like terms: -6.557438524 + -1 = -7.557438524 s = -7.557438524 Simplifying s = -7.557438524Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.557438524, -7.557438524}
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