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Simplifying 5s2 = 36s + -32 Reorder the terms: 5s2 = -32 + 36s Solving 5s2 = -32 + 36s Solving for variable 's'. Reorder the terms: 32 + -36s + 5s2 = -32 + 36s + 32 + -36s Reorder the terms: 32 + -36s + 5s2 = -32 + 32 + 36s + -36s Combine like terms: -32 + 32 = 0 32 + -36s + 5s2 = 0 + 36s + -36s 32 + -36s + 5s2 = 36s + -36s Combine like terms: 36s + -36s = 0 32 + -36s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.4 + -7.2s + s2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + -7.2s + -6.4 + s2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + -7.2s + s2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + -7.2s + s2 = 0 + -6.4 -7.2s + s2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 -7.2s + s2 = -6.4 The s term is -7.2s. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2s + 12.96 + s2 = -6.4 + 12.96 Reorder the terms: 12.96 + -7.2s + s2 = -6.4 + 12.96 Combine like terms: -6.4 + 12.96 = 6.56 12.96 + -7.2s + s2 = 6.56 Factor a perfect square on the left side: (s + -3.6)(s + -3.6) = 6.56 Calculate the square root of the right side: 2.561249695 Break this problem into two subproblems by setting (s + -3.6) equal to 2.561249695 and -2.561249695.Subproblem 1
s + -3.6 = 2.561249695 Simplifying s + -3.6 = 2.561249695 Reorder the terms: -3.6 + s = 2.561249695 Solving -3.6 + s = 2.561249695 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + s = 2.561249695 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + s = 2.561249695 + 3.6 s = 2.561249695 + 3.6 Combine like terms: 2.561249695 + 3.6 = 6.161249695 s = 6.161249695 Simplifying s = 6.161249695Subproblem 2
s + -3.6 = -2.561249695 Simplifying s + -3.6 = -2.561249695 Reorder the terms: -3.6 + s = -2.561249695 Solving -3.6 + s = -2.561249695 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + s = -2.561249695 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + s = -2.561249695 + 3.6 s = -2.561249695 + 3.6 Combine like terms: -2.561249695 + 3.6 = 1.038750305 s = 1.038750305 Simplifying s = 1.038750305Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.161249695, 1.038750305}
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