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Simplifying 4s2 + -5s = 5 Reorder the terms: -5s + 4s2 = 5 Solving -5s + 4s2 = 5 Solving for variable 's'. Reorder the terms: -5 + -5s + 4s2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -5s + 4s2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1.25s + s2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.25s + 1.25 + s2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.25s + s2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.25s + s2 = 0 + 1.25 -1.25s + s2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.25s + s2 = 1.25 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 = 1.25 + 0.390625 Reorder the terms: 0.390625 + -1.25s + s2 = 1.25 + 0.390625 Combine like terms: 1.25 + 0.390625 = 1.640625 0.390625 + -1.25s + s2 = 1.640625 Factor a perfect square on the left side: (s + -0.625)(s + -0.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (s + -0.625) equal to 1.280868846 and -1.280868846.Subproblem 1
s + -0.625 = 1.280868846 Simplifying s + -0.625 = 1.280868846 Reorder the terms: -0.625 + s = 1.280868846 Solving -0.625 + s = 1.280868846 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 = 1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + s = 1.280868846 + 0.625 s = 1.280868846 + 0.625 Combine like terms: 1.280868846 + 0.625 = 1.905868846 s = 1.905868846 Simplifying s = 1.905868846Subproblem 2
s + -0.625 = -1.280868846 Simplifying s + -0.625 = -1.280868846 Reorder the terms: -0.625 + s = -1.280868846 Solving -0.625 + s = -1.280868846 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 = -1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + s = -1.280868846 + 0.625 s = -1.280868846 + 0.625 Combine like terms: -1.280868846 + 0.625 = -0.655868846 s = -0.655868846 Simplifying s = -0.655868846Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.905868846, -0.655868846}
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