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Simplifying 9s2 + -29s + 2 = 0 Reorder the terms: 2 + -29s + 9s2 = 0 Solving 2 + -29s + 9s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -3.222222222s + s2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -3.222222222s + -0.2222222222 + s2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -3.222222222s + s2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -3.222222222s + s2 = 0 + -0.2222222222 -3.222222222s + s2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -3.222222222s + s2 = -0.2222222222 The s term is -3.222222222s. Take half its coefficient (-1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. -3.222222222s + 2.595679012 + s2 = -0.2222222222 + 2.595679012 Reorder the terms: 2.595679012 + -3.222222222s + s2 = -0.2222222222 + 2.595679012 Combine like terms: -0.2222222222 + 2.595679012 = 2.3734567898 2.595679012 + -3.222222222s + s2 = 2.3734567898 Factor a perfect square on the left side: (s + -1.611111111)(s + -1.611111111) = 2.3734567898 Calculate the square root of the right side: 1.540602736 Break this problem into two subproblems by setting (s + -1.611111111) equal to 1.540602736 and -1.540602736.Subproblem 1
s + -1.611111111 = 1.540602736 Simplifying s + -1.611111111 = 1.540602736 Reorder the terms: -1.611111111 + s = 1.540602736 Solving -1.611111111 + s = 1.540602736 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + s = 1.540602736 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + s = 1.540602736 + 1.611111111 s = 1.540602736 + 1.611111111 Combine like terms: 1.540602736 + 1.611111111 = 3.151713847 s = 3.151713847 Simplifying s = 3.151713847Subproblem 2
s + -1.611111111 = -1.540602736 Simplifying s + -1.611111111 = -1.540602736 Reorder the terms: -1.611111111 + s = -1.540602736 Solving -1.611111111 + s = -1.540602736 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + s = -1.540602736 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + s = -1.540602736 + 1.611111111 s = -1.540602736 + 1.611111111 Combine like terms: -1.540602736 + 1.611111111 = 0.070508375 s = 0.070508375 Simplifying s = 0.070508375Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.151713847, 0.070508375}
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