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Simplifying 64s2 + 144s = 81 Reorder the terms: 144s + 64s2 = 81 Solving 144s + 64s2 = 81 Solving for variable 's'. Reorder the terms: -81 + 144s + 64s2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 144s + 64s2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -1.265625 + 2.25s + s2 = 0 Move the constant term to the right: Add '1.265625' to each side of the equation. -1.265625 + 2.25s + 1.265625 + s2 = 0 + 1.265625 Reorder the terms: -1.265625 + 1.265625 + 2.25s + s2 = 0 + 1.265625 Combine like terms: -1.265625 + 1.265625 = 0.000000 0.000000 + 2.25s + s2 = 0 + 1.265625 2.25s + s2 = 0 + 1.265625 Combine like terms: 0 + 1.265625 = 1.265625 2.25s + s2 = 1.265625 The s term is 2.25s. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25s + 1.265625 + s2 = 1.265625 + 1.265625 Reorder the terms: 1.265625 + 2.25s + s2 = 1.265625 + 1.265625 Combine like terms: 1.265625 + 1.265625 = 2.53125 1.265625 + 2.25s + s2 = 2.53125 Factor a perfect square on the left side: (s + 1.125)(s + 1.125) = 2.53125 Calculate the square root of the right side: 1.590990258 Break this problem into two subproblems by setting (s + 1.125) equal to 1.590990258 and -1.590990258.Subproblem 1
s + 1.125 = 1.590990258 Simplifying s + 1.125 = 1.590990258 Reorder the terms: 1.125 + s = 1.590990258 Solving 1.125 + s = 1.590990258 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + s = 1.590990258 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + s = 1.590990258 + -1.125 s = 1.590990258 + -1.125 Combine like terms: 1.590990258 + -1.125 = 0.465990258 s = 0.465990258 Simplifying s = 0.465990258Subproblem 2
s + 1.125 = -1.590990258 Simplifying s + 1.125 = -1.590990258 Reorder the terms: 1.125 + s = -1.590990258 Solving 1.125 + s = -1.590990258 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + s = -1.590990258 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + s = -1.590990258 + -1.125 s = -1.590990258 + -1.125 Combine like terms: -1.590990258 + -1.125 = -2.715990258 s = -2.715990258 Simplifying s = -2.715990258Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.465990258, -2.715990258}
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