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Simplifying C2 + 10C = 10 Reorder the terms: 10C + C2 = 10 Solving 10C + C2 = 10 Solving for variable 'C'. Reorder the terms: -10 + 10C + C2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 10C + C2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 10C + 10 + C2 = 0 + 10 Reorder the terms: -10 + 10 + 10C + C2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10C + C2 = 0 + 10 10C + C2 = 0 + 10 Combine like terms: 0 + 10 = 10 10C + C2 = 10 The C term is 10C. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10C + 25 + C2 = 10 + 25 Reorder the terms: 25 + 10C + C2 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + 10C + C2 = 35 Factor a perfect square on the left side: (C + 5)(C + 5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (C + 5) equal to 5.916079783 and -5.916079783.Subproblem 1
C + 5 = 5.916079783 Simplifying C + 5 = 5.916079783 Reorder the terms: 5 + C = 5.916079783 Solving 5 + C = 5.916079783 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + C = 5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + C = 5.916079783 + -5 C = 5.916079783 + -5 Combine like terms: 5.916079783 + -5 = 0.916079783 C = 0.916079783 Simplifying C = 0.916079783Subproblem 2
C + 5 = -5.916079783 Simplifying C + 5 = -5.916079783 Reorder the terms: 5 + C = -5.916079783 Solving 5 + C = -5.916079783 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + C = -5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + C = -5.916079783 + -5 C = -5.916079783 + -5 Combine like terms: -5.916079783 + -5 = -10.916079783 C = -10.916079783 Simplifying C = -10.916079783Solution
The solution to the problem is based on the solutions from the subproblems. C = {0.916079783, -10.916079783}
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