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Simplifying s2 + -7s = 48 Reorder the terms: -7s + s2 = 48 Solving -7s + s2 = 48 Solving for variable 's'. Reorder the terms: -48 + -7s + s2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -7s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -7s + 48 + s2 = 0 + 48 Reorder the terms: -48 + 48 + -7s + s2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -7s + s2 = 0 + 48 -7s + s2 = 0 + 48 Combine like terms: 0 + 48 = 48 -7s + s2 = 48 The s term is -7s. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7s + 12.25 + s2 = 48 + 12.25 Reorder the terms: 12.25 + -7s + s2 = 48 + 12.25 Combine like terms: 48 + 12.25 = 60.25 12.25 + -7s + s2 = 60.25 Factor a perfect square on the left side: (s + -3.5)(s + -3.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (s + -3.5) equal to 7.762087348 and -7.762087348.Subproblem 1
s + -3.5 = 7.762087348 Simplifying s + -3.5 = 7.762087348 Reorder the terms: -3.5 + s = 7.762087348 Solving -3.5 + s = 7.762087348 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + s = 7.762087348 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + s = 7.762087348 + 3.5 s = 7.762087348 + 3.5 Combine like terms: 7.762087348 + 3.5 = 11.262087348 s = 11.262087348 Simplifying s = 11.262087348Subproblem 2
s + -3.5 = -7.762087348 Simplifying s + -3.5 = -7.762087348 Reorder the terms: -3.5 + s = -7.762087348 Solving -3.5 + s = -7.762087348 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + s = -7.762087348 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + s = -7.762087348 + 3.5 s = -7.762087348 + 3.5 Combine like terms: -7.762087348 + 3.5 = -4.262087348 s = -4.262087348 Simplifying s = -4.262087348Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.262087348, -4.262087348}
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