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Simplifying c2 + -101c = -25 Reorder the terms: -101c + c2 = -25 Solving -101c + c2 = -25 Solving for variable 'c'. Reorder the terms: 25 + -101c + c2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -101c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -101c + -25 + c2 = 0 + -25 Reorder the terms: 25 + -25 + -101c + c2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -101c + c2 = 0 + -25 -101c + c2 = 0 + -25 Combine like terms: 0 + -25 = -25 -101c + c2 = -25 The c term is -101c. Take half its coefficient (-50.5). Square it (2550.25) and add it to both sides. Add '2550.25' to each side of the equation. -101c + 2550.25 + c2 = -25 + 2550.25 Reorder the terms: 2550.25 + -101c + c2 = -25 + 2550.25 Combine like terms: -25 + 2550.25 = 2525.25 2550.25 + -101c + c2 = 2525.25 Factor a perfect square on the left side: (c + -50.5)(c + -50.5) = 2525.25 Calculate the square root of the right side: 50.251865637 Break this problem into two subproblems by setting (c + -50.5) equal to 50.251865637 and -50.251865637.Subproblem 1
c + -50.5 = 50.251865637 Simplifying c + -50.5 = 50.251865637 Reorder the terms: -50.5 + c = 50.251865637 Solving -50.5 + c = 50.251865637 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '50.5' to each side of the equation. -50.5 + 50.5 + c = 50.251865637 + 50.5 Combine like terms: -50.5 + 50.5 = 0.0 0.0 + c = 50.251865637 + 50.5 c = 50.251865637 + 50.5 Combine like terms: 50.251865637 + 50.5 = 100.751865637 c = 100.751865637 Simplifying c = 100.751865637Subproblem 2
c + -50.5 = -50.251865637 Simplifying c + -50.5 = -50.251865637 Reorder the terms: -50.5 + c = -50.251865637 Solving -50.5 + c = -50.251865637 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '50.5' to each side of the equation. -50.5 + 50.5 + c = -50.251865637 + 50.5 Combine like terms: -50.5 + 50.5 = 0.0 0.0 + c = -50.251865637 + 50.5 c = -50.251865637 + 50.5 Combine like terms: -50.251865637 + 50.5 = 0.248134363 c = 0.248134363 Simplifying c = 0.248134363Solution
The solution to the problem is based on the solutions from the subproblems. c = {100.751865637, 0.248134363}
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