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Simplifying s2 = 3 + 5s + -6s2 Solving s2 = 3 + 5s + -6s2 Solving for variable 's'. Reorder the terms: -3 + -5s + s2 + 6s2 = 3 + 5s + -6s2 + -3 + -5s + 6s2 Combine like terms: s2 + 6s2 = 7s2 -3 + -5s + 7s2 = 3 + 5s + -6s2 + -3 + -5s + 6s2 Reorder the terms: -3 + -5s + 7s2 = 3 + -3 + 5s + -5s + -6s2 + 6s2 Combine like terms: 3 + -3 = 0 -3 + -5s + 7s2 = 0 + 5s + -5s + -6s2 + 6s2 -3 + -5s + 7s2 = 5s + -5s + -6s2 + 6s2 Combine like terms: 5s + -5s = 0 -3 + -5s + 7s2 = 0 + -6s2 + 6s2 -3 + -5s + 7s2 = -6s2 + 6s2 Combine like terms: -6s2 + 6s2 = 0 -3 + -5s + 7s2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -0.7142857143s + s2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.7142857143s + 0.4285714286 + s2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.7142857143s + s2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.7142857143s + s2 = 0 + 0.4285714286 -0.7142857143s + s2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.7142857143s + s2 = 0.4285714286 The s term is -0.7142857143s. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143s + 0.1275510204 + s2 = 0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143s + s2 = 0.4285714286 + 0.1275510204 Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449 0.1275510204 + -0.7142857143s + s2 = 0.556122449 Factor a perfect square on the left side: (s + -0.3571428572)(s + -0.3571428572) = 0.556122449 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (s + -0.3571428572) equal to 0.745736179 and -0.745736179.Subproblem 1
s + -0.3571428572 = 0.745736179 Simplifying s + -0.3571428572 = 0.745736179 Reorder the terms: -0.3571428572 + s = 0.745736179 Solving -0.3571428572 + s = 0.745736179 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + s = 0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + s = 0.745736179 + 0.3571428572 s = 0.745736179 + 0.3571428572 Combine like terms: 0.745736179 + 0.3571428572 = 1.1028790362 s = 1.1028790362 Simplifying s = 1.1028790362Subproblem 2
s + -0.3571428572 = -0.745736179 Simplifying s + -0.3571428572 = -0.745736179 Reorder the terms: -0.3571428572 + s = -0.745736179 Solving -0.3571428572 + s = -0.745736179 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + s = -0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + s = -0.745736179 + 0.3571428572 s = -0.745736179 + 0.3571428572 Combine like terms: -0.745736179 + 0.3571428572 = -0.3885933218 s = -0.3885933218 Simplifying s = -0.3885933218Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.1028790362, -0.3885933218}
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