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Simplifying 81s2 + 36s = 4 Reorder the terms: 36s + 81s2 = 4 Solving 36s + 81s2 = 4 Solving for variable 's'. Reorder the terms: -4 + 36s + 81s2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 36s + 81s2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.04938271605 + 0.4444444444s + s2 = 0 Move the constant term to the right: Add '0.04938271605' to each side of the equation. -0.04938271605 + 0.4444444444s + 0.04938271605 + s2 = 0 + 0.04938271605 Reorder the terms: -0.04938271605 + 0.04938271605 + 0.4444444444s + s2 = 0 + 0.04938271605 Combine like terms: -0.04938271605 + 0.04938271605 = 0.00000000000 0.00000000000 + 0.4444444444s + s2 = 0 + 0.04938271605 0.4444444444s + s2 = 0 + 0.04938271605 Combine like terms: 0 + 0.04938271605 = 0.04938271605 0.4444444444s + s2 = 0.04938271605 The s term is 0.4444444444s. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444s + 0.04938271604 + s2 = 0.04938271605 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444s + s2 = 0.04938271605 + 0.04938271604 Combine like terms: 0.04938271605 + 0.04938271604 = 0.09876543209 0.04938271604 + 0.4444444444s + s2 = 0.09876543209 Factor a perfect square on the left side: (s + 0.2222222222)(s + 0.2222222222) = 0.09876543209 Calculate the square root of the right side: 0.314269681 Break this problem into two subproblems by setting (s + 0.2222222222) equal to 0.314269681 and -0.314269681.Subproblem 1
s + 0.2222222222 = 0.314269681 Simplifying s + 0.2222222222 = 0.314269681 Reorder the terms: 0.2222222222 + s = 0.314269681 Solving 0.2222222222 + s = 0.314269681 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + s = 0.314269681 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + s = 0.314269681 + -0.2222222222 s = 0.314269681 + -0.2222222222 Combine like terms: 0.314269681 + -0.2222222222 = 0.0920474588 s = 0.0920474588 Simplifying s = 0.0920474588Subproblem 2
s + 0.2222222222 = -0.314269681 Simplifying s + 0.2222222222 = -0.314269681 Reorder the terms: 0.2222222222 + s = -0.314269681 Solving 0.2222222222 + s = -0.314269681 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + s = -0.314269681 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + s = -0.314269681 + -0.2222222222 s = -0.314269681 + -0.2222222222 Combine like terms: -0.314269681 + -0.2222222222 = -0.5364919032 s = -0.5364919032 Simplifying s = -0.5364919032Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.0920474588, -0.5364919032}
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