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Simplifying s2 + 8s + -125 = 0 Reorder the terms: -125 + 8s + s2 = 0 Solving -125 + 8s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 8s + 125 + s2 = 0 + 125 Reorder the terms: -125 + 125 + 8s + s2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 8s + s2 = 0 + 125 8s + s2 = 0 + 125 Combine like terms: 0 + 125 = 125 8s + s2 = 125 The s term is 8s. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8s + 16 + s2 = 125 + 16 Reorder the terms: 16 + 8s + s2 = 125 + 16 Combine like terms: 125 + 16 = 141 16 + 8s + s2 = 141 Factor a perfect square on the left side: (s + 4)(s + 4) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (s + 4) equal to 11.874342087 and -11.874342087.Subproblem 1
s + 4 = 11.874342087 Simplifying s + 4 = 11.874342087 Reorder the terms: 4 + s = 11.874342087 Solving 4 + s = 11.874342087 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + s = 11.874342087 + -4 Combine like terms: 4 + -4 = 0 0 + s = 11.874342087 + -4 s = 11.874342087 + -4 Combine like terms: 11.874342087 + -4 = 7.874342087 s = 7.874342087 Simplifying s = 7.874342087Subproblem 2
s + 4 = -11.874342087 Simplifying s + 4 = -11.874342087 Reorder the terms: 4 + s = -11.874342087 Solving 4 + s = -11.874342087 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + s = -11.874342087 + -4 Combine like terms: 4 + -4 = 0 0 + s = -11.874342087 + -4 s = -11.874342087 + -4 Combine like terms: -11.874342087 + -4 = -15.874342087 s = -15.874342087 Simplifying s = -15.874342087Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.874342087, -15.874342087}
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