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Simplifying s2 + -8s + 2 = 0 Reorder the terms: 2 + -8s + s2 = 0 Solving 2 + -8s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -8s + -2 + s2 = 0 + -2 Reorder the terms: 2 + -2 + -8s + s2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -8s + s2 = 0 + -2 -8s + s2 = 0 + -2 Combine like terms: 0 + -2 = -2 -8s + s2 = -2 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 = -2 + 16 Reorder the terms: 16 + -8s + s2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + -8s + s2 = 14 Factor a perfect square on the left side: (s + -4)(s + -4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (s + -4) equal to 3.741657387 and -3.741657387.Subproblem 1
s + -4 = 3.741657387 Simplifying s + -4 = 3.741657387 Reorder the terms: -4 + s = 3.741657387 Solving -4 + s = 3.741657387 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 = 3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + s = 3.741657387 + 4 s = 3.741657387 + 4 Combine like terms: 3.741657387 + 4 = 7.741657387 s = 7.741657387 Simplifying s = 7.741657387Subproblem 2
s + -4 = -3.741657387 Simplifying s + -4 = -3.741657387 Reorder the terms: -4 + s = -3.741657387 Solving -4 + s = -3.741657387 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 = -3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + s = -3.741657387 + 4 s = -3.741657387 + 4 Combine like terms: -3.741657387 + 4 = 0.258342613 s = 0.258342613 Simplifying s = 0.258342613Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.741657387, 0.258342613}
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