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Simplifying 2s2 = 35 + -2s Solving 2s2 = 35 + -2s Solving for variable 's'. Reorder the terms: -35 + 2s + 2s2 = 35 + -2s + -35 + 2s Reorder the terms: -35 + 2s + 2s2 = 35 + -35 + -2s + 2s Combine like terms: 35 + -35 = 0 -35 + 2s + 2s2 = 0 + -2s + 2s -35 + 2s + 2s2 = -2s + 2s Combine like terms: -2s + 2s = 0 -35 + 2s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + s + s2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + s + 17.5 + s2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + s + s2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + s + s2 = 0 + 17.5 s + s2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 s + s2 = 17.5 The s term is s. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + s2 = 17.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + s2 = 17.5 + 0.25 Combine like terms: 17.5 + 0.25 = 17.75 1.25 + s2 = 17.75 Factor a perfect square on the left side: (s + 0.5)(s + 0.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (s + 0.5) equal to 4.213074887 and -4.213074887.Subproblem 1
s + 0.5 = 4.213074887 Simplifying s + 0.5 = 4.213074887 Reorder the terms: 0.5 + s = 4.213074887 Solving 0.5 + s = 4.213074887 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + s = 4.213074887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + s = 4.213074887 + -0.5 s = 4.213074887 + -0.5 Combine like terms: 4.213074887 + -0.5 = 3.713074887 s = 3.713074887 Simplifying s = 3.713074887Subproblem 2
s + 0.5 = -4.213074887 Simplifying s + 0.5 = -4.213074887 Reorder the terms: 0.5 + s = -4.213074887 Solving 0.5 + s = -4.213074887 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + s = -4.213074887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + s = -4.213074887 + -0.5 s = -4.213074887 + -0.5 Combine like terms: -4.213074887 + -0.5 = -4.713074887 s = -4.713074887 Simplifying s = -4.713074887Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.713074887, -4.713074887}
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