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Simplifying 49s2 + 122s = -64 Reorder the terms: 122s + 49s2 = -64 Solving 122s + 49s2 = -64 Solving for variable 's'. Reorder the terms: 64 + 122s + 49s2 = -64 + 64 Combine like terms: -64 + 64 = 0 64 + 122s + 49s2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 1.306122449 + 2.489795918s + s2 = 0 Move the constant term to the right: Add '-1.306122449' to each side of the equation. 1.306122449 + 2.489795918s + -1.306122449 + s2 = 0 + -1.306122449 Reorder the terms: 1.306122449 + -1.306122449 + 2.489795918s + s2 = 0 + -1.306122449 Combine like terms: 1.306122449 + -1.306122449 = 0.000000000 0.000000000 + 2.489795918s + s2 = 0 + -1.306122449 2.489795918s + s2 = 0 + -1.306122449 Combine like terms: 0 + -1.306122449 = -1.306122449 2.489795918s + s2 = -1.306122449 The s term is 2.489795918s. Take half its coefficient (1.244897959). Square it (1.549770928) and add it to both sides. Add '1.549770928' to each side of the equation. 2.489795918s + 1.549770928 + s2 = -1.306122449 + 1.549770928 Reorder the terms: 1.549770928 + 2.489795918s + s2 = -1.306122449 + 1.549770928 Combine like terms: -1.306122449 + 1.549770928 = 0.243648479 1.549770928 + 2.489795918s + s2 = 0.243648479 Factor a perfect square on the left side: (s + 1.244897959)(s + 1.244897959) = 0.243648479 Calculate the square root of the right side: 0.493607616 Break this problem into two subproblems by setting (s + 1.244897959) equal to 0.493607616 and -0.493607616.Subproblem 1
s + 1.244897959 = 0.493607616 Simplifying s + 1.244897959 = 0.493607616 Reorder the terms: 1.244897959 + s = 0.493607616 Solving 1.244897959 + s = 0.493607616 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.244897959' to each side of the equation. 1.244897959 + -1.244897959 + s = 0.493607616 + -1.244897959 Combine like terms: 1.244897959 + -1.244897959 = 0.000000000 0.000000000 + s = 0.493607616 + -1.244897959 s = 0.493607616 + -1.244897959 Combine like terms: 0.493607616 + -1.244897959 = -0.751290343 s = -0.751290343 Simplifying s = -0.751290343Subproblem 2
s + 1.244897959 = -0.493607616 Simplifying s + 1.244897959 = -0.493607616 Reorder the terms: 1.244897959 + s = -0.493607616 Solving 1.244897959 + s = -0.493607616 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.244897959' to each side of the equation. 1.244897959 + -1.244897959 + s = -0.493607616 + -1.244897959 Combine like terms: 1.244897959 + -1.244897959 = 0.000000000 0.000000000 + s = -0.493607616 + -1.244897959 s = -0.493607616 + -1.244897959 Combine like terms: -0.493607616 + -1.244897959 = -1.738505575 s = -1.738505575 Simplifying s = -1.738505575Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.751290343, -1.738505575}
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