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Simplifying s2 + -8s + -8 = 0 Reorder the terms: -8 + -8s + s2 = 0 Solving -8 + -8s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -8s + 8 + s2 = 0 + 8 Reorder the terms: -8 + 8 + -8s + s2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8s + s2 = 0 + 8 -8s + s2 = 0 + 8 Combine like terms: 0 + 8 = 8 -8s + s2 = 8 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 = 8 + 16 Reorder the terms: 16 + -8s + s2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + -8s + s2 = 24 Factor a perfect square on the left side: (s + -4)(s + -4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (s + -4) equal to 4.898979486 and -4.898979486.Subproblem 1
s + -4 = 4.898979486 Simplifying s + -4 = 4.898979486 Reorder the terms: -4 + s = 4.898979486 Solving -4 + s = 4.898979486 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 = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + s = 4.898979486 + 4 s = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 s = 8.898979486 Simplifying s = 8.898979486Subproblem 2
s + -4 = -4.898979486 Simplifying s + -4 = -4.898979486 Reorder the terms: -4 + s = -4.898979486 Solving -4 + s = -4.898979486 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 = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + s = -4.898979486 + 4 s = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 s = -0.898979486 Simplifying s = -0.898979486Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.898979486, -0.898979486}
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