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Simplifying C2 + -24C = 255 Reorder the terms: -24C + C2 = 255 Solving -24C + C2 = 255 Solving for variable 'C'. Reorder the terms: -255 + -24C + C2 = 255 + -255 Combine like terms: 255 + -255 = 0 -255 + -24C + C2 = 0 Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + -24C + 255 + C2 = 0 + 255 Reorder the terms: -255 + 255 + -24C + C2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + -24C + C2 = 0 + 255 -24C + C2 = 0 + 255 Combine like terms: 0 + 255 = 255 -24C + C2 = 255 The C term is -24C. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24C + 144 + C2 = 255 + 144 Reorder the terms: 144 + -24C + C2 = 255 + 144 Combine like terms: 255 + 144 = 399 144 + -24C + C2 = 399 Factor a perfect square on the left side: (C + -12)(C + -12) = 399 Calculate the square root of the right side: 19.974984355 Break this problem into two subproblems by setting (C + -12) equal to 19.974984355 and -19.974984355.Subproblem 1
C + -12 = 19.974984355 Simplifying C + -12 = 19.974984355 Reorder the terms: -12 + C = 19.974984355 Solving -12 + C = 19.974984355 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + C = 19.974984355 + 12 Combine like terms: -12 + 12 = 0 0 + C = 19.974984355 + 12 C = 19.974984355 + 12 Combine like terms: 19.974984355 + 12 = 31.974984355 C = 31.974984355 Simplifying C = 31.974984355Subproblem 2
C + -12 = -19.974984355 Simplifying C + -12 = -19.974984355 Reorder the terms: -12 + C = -19.974984355 Solving -12 + C = -19.974984355 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + C = -19.974984355 + 12 Combine like terms: -12 + 12 = 0 0 + C = -19.974984355 + 12 C = -19.974984355 + 12 Combine like terms: -19.974984355 + 12 = -7.974984355 C = -7.974984355 Simplifying C = -7.974984355Solution
The solution to the problem is based on the solutions from the subproblems. C = {31.974984355, -7.974984355}
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