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Simplifying 4s2 + -10s + 5 = 0 Reorder the terms: 5 + -10s + 4s2 = 0 Solving 5 + -10s + 4s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -2.5s + s2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.5s + -1.25 + s2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.5s + s2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.5s + s2 = 0 + -1.25 -2.5s + s2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.5s + s2 = -1.25 The s term is -2.5s. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5s + 1.5625 + s2 = -1.25 + 1.5625 Reorder the terms: 1.5625 + -2.5s + s2 = -1.25 + 1.5625 Combine like terms: -1.25 + 1.5625 = 0.3125 1.5625 + -2.5s + s2 = 0.3125 Factor a perfect square on the left side: (s + -1.25)(s + -1.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (s + -1.25) equal to 0.559016994 and -0.559016994.Subproblem 1
s + -1.25 = 0.559016994 Simplifying s + -1.25 = 0.559016994 Reorder the terms: -1.25 + s = 0.559016994 Solving -1.25 + s = 0.559016994 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + s = 0.559016994 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + s = 0.559016994 + 1.25 s = 0.559016994 + 1.25 Combine like terms: 0.559016994 + 1.25 = 1.809016994 s = 1.809016994 Simplifying s = 1.809016994Subproblem 2
s + -1.25 = -0.559016994 Simplifying s + -1.25 = -0.559016994 Reorder the terms: -1.25 + s = -0.559016994 Solving -1.25 + s = -0.559016994 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + s = -0.559016994 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + s = -0.559016994 + 1.25 s = -0.559016994 + 1.25 Combine like terms: -0.559016994 + 1.25 = 0.690983006 s = 0.690983006 Simplifying s = 0.690983006Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.809016994, 0.690983006}
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