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Simplifying 64s2 + 80s = 25 Reorder the terms: 80s + 64s2 = 25 Solving 80s + 64s2 = 25 Solving for variable 's'. Reorder the terms: -25 + 80s + 64s2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 80s + 64s2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.390625 + 1.25s + s2 = 0 Move the constant term to the right: Add '0.390625' to each side of the equation. -0.390625 + 1.25s + 0.390625 + s2 = 0 + 0.390625 Reorder the terms: -0.390625 + 0.390625 + 1.25s + s2 = 0 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.000000 + 1.25s + s2 = 0 + 0.390625 1.25s + s2 = 0 + 0.390625 Combine like terms: 0 + 0.390625 = 0.390625 1.25s + s2 = 0.390625 The s term is 1.25s. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25s + 0.390625 + s2 = 0.390625 + 0.390625 Reorder the terms: 0.390625 + 1.25s + s2 = 0.390625 + 0.390625 Combine like terms: 0.390625 + 0.390625 = 0.78125 0.390625 + 1.25s + s2 = 0.78125 Factor a perfect square on the left side: (s + 0.625)(s + 0.625) = 0.78125 Calculate the square root of the right side: 0.883883476 Break this problem into two subproblems by setting (s + 0.625) equal to 0.883883476 and -0.883883476.Subproblem 1
s + 0.625 = 0.883883476 Simplifying s + 0.625 = 0.883883476 Reorder the terms: 0.625 + s = 0.883883476 Solving 0.625 + s = 0.883883476 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + s = 0.883883476 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + s = 0.883883476 + -0.625 s = 0.883883476 + -0.625 Combine like terms: 0.883883476 + -0.625 = 0.258883476 s = 0.258883476 Simplifying s = 0.258883476Subproblem 2
s + 0.625 = -0.883883476 Simplifying s + 0.625 = -0.883883476 Reorder the terms: 0.625 + s = -0.883883476 Solving 0.625 + s = -0.883883476 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + s = -0.883883476 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + s = -0.883883476 + -0.625 s = -0.883883476 + -0.625 Combine like terms: -0.883883476 + -0.625 = -1.508883476 s = -1.508883476 Simplifying s = -1.508883476Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.258883476, -1.508883476}
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