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Simplifying c2 + 1 = 12c Reorder the terms: 1 + c2 = 12c Solving 1 + c2 = 12c Solving for variable 'c'. Reorder the terms: 1 + -12c + c2 = 12c + -12c Combine like terms: 12c + -12c = 0 1 + -12c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -12c + -1 + c2 = 0 + -1 Reorder the terms: 1 + -1 + -12c + c2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12c + c2 = 0 + -1 -12c + c2 = 0 + -1 Combine like terms: 0 + -1 = -1 -12c + c2 = -1 The c term is -12c. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12c + 36 + c2 = -1 + 36 Reorder the terms: 36 + -12c + c2 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + -12c + c2 = 35 Factor a perfect square on the left side: (c + -6)(c + -6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (c + -6) equal to 5.916079783 and -5.916079783.Subproblem 1
c + -6 = 5.916079783 Simplifying c + -6 = 5.916079783 Reorder the terms: -6 + c = 5.916079783 Solving -6 + c = 5.916079783 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + c = 5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + c = 5.916079783 + 6 c = 5.916079783 + 6 Combine like terms: 5.916079783 + 6 = 11.916079783 c = 11.916079783 Simplifying c = 11.916079783Subproblem 2
c + -6 = -5.916079783 Simplifying c + -6 = -5.916079783 Reorder the terms: -6 + c = -5.916079783 Solving -6 + c = -5.916079783 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + c = -5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + c = -5.916079783 + 6 c = -5.916079783 + 6 Combine like terms: -5.916079783 + 6 = 0.083920217 c = 0.083920217 Simplifying c = 0.083920217Solution
The solution to the problem is based on the solutions from the subproblems. c = {11.916079783, 0.083920217}
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