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Simplifying c2 + -81c + 81 = 0 Reorder the terms: 81 + -81c + c2 = 0 Solving 81 + -81c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -81c + -81 + c2 = 0 + -81 Reorder the terms: 81 + -81 + -81c + c2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -81c + c2 = 0 + -81 -81c + c2 = 0 + -81 Combine like terms: 0 + -81 = -81 -81c + c2 = -81 The c term is -81c. Take half its coefficient (-40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. -81c + 1640.25 + c2 = -81 + 1640.25 Reorder the terms: 1640.25 + -81c + c2 = -81 + 1640.25 Combine like terms: -81 + 1640.25 = 1559.25 1640.25 + -81c + c2 = 1559.25 Factor a perfect square on the left side: (c + -40.5)(c + -40.5) = 1559.25 Calculate the square root of the right side: 39.487339743 Break this problem into two subproblems by setting (c + -40.5) equal to 39.487339743 and -39.487339743.Subproblem 1
c + -40.5 = 39.487339743 Simplifying c + -40.5 = 39.487339743 Reorder the terms: -40.5 + c = 39.487339743 Solving -40.5 + c = 39.487339743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + c = 39.487339743 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + c = 39.487339743 + 40.5 c = 39.487339743 + 40.5 Combine like terms: 39.487339743 + 40.5 = 79.987339743 c = 79.987339743 Simplifying c = 79.987339743Subproblem 2
c + -40.5 = -39.487339743 Simplifying c + -40.5 = -39.487339743 Reorder the terms: -40.5 + c = -39.487339743 Solving -40.5 + c = -39.487339743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + c = -39.487339743 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + c = -39.487339743 + 40.5 c = -39.487339743 + 40.5 Combine like terms: -39.487339743 + 40.5 = 1.012660257 c = 1.012660257 Simplifying c = 1.012660257Solution
The solution to the problem is based on the solutions from the subproblems. c = {79.987339743, 1.012660257}
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