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Simplifying 9s2 + 3s + -4 = 0 Reorder the terms: -4 + 3s + 9s2 = 0 Solving -4 + 3s + 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'. -0.4444444444 + 0.3333333333s + s2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.3333333333s + 0.4444444444 + s2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.3333333333s + s2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.3333333333s + s2 = 0 + 0.4444444444 0.3333333333s + s2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.3333333333s + s2 = 0.4444444444 The s term is 0.3333333333s. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333s + 0.02777777779 + s2 = 0.4444444444 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333s + s2 = 0.4444444444 + 0.02777777779 Combine like terms: 0.4444444444 + 0.02777777779 = 0.47222222219 0.02777777779 + 0.3333333333s + s2 = 0.47222222219 Factor a perfect square on the left side: (s + 0.1666666667)(s + 0.1666666667) = 0.47222222219 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (s + 0.1666666667) equal to 0.687184271 and -0.687184271.Subproblem 1
s + 0.1666666667 = 0.687184271 Simplifying s + 0.1666666667 = 0.687184271 Reorder the terms: 0.1666666667 + s = 0.687184271 Solving 0.1666666667 + s = 0.687184271 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + s = 0.687184271 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + s = 0.687184271 + -0.1666666667 s = 0.687184271 + -0.1666666667 Combine like terms: 0.687184271 + -0.1666666667 = 0.5205176043 s = 0.5205176043 Simplifying s = 0.5205176043Subproblem 2
s + 0.1666666667 = -0.687184271 Simplifying s + 0.1666666667 = -0.687184271 Reorder the terms: 0.1666666667 + s = -0.687184271 Solving 0.1666666667 + s = -0.687184271 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + s = -0.687184271 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + s = -0.687184271 + -0.1666666667 s = -0.687184271 + -0.1666666667 Combine like terms: -0.687184271 + -0.1666666667 = -0.8538509377 s = -0.8538509377 Simplifying s = -0.8538509377Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.5205176043, -0.8538509377}
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