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Simplifying c2 + -26c = 18 Reorder the terms: -26c + c2 = 18 Solving -26c + c2 = 18 Solving for variable 'c'. Reorder the terms: -18 + -26c + c2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -26c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -26c + 18 + c2 = 0 + 18 Reorder the terms: -18 + 18 + -26c + c2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -26c + c2 = 0 + 18 -26c + c2 = 0 + 18 Combine like terms: 0 + 18 = 18 -26c + c2 = 18 The c term is -26c. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26c + 169 + c2 = 18 + 169 Reorder the terms: 169 + -26c + c2 = 18 + 169 Combine like terms: 18 + 169 = 187 169 + -26c + c2 = 187 Factor a perfect square on the left side: (c + -13)(c + -13) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (c + -13) equal to 13.674794331 and -13.674794331.Subproblem 1
c + -13 = 13.674794331 Simplifying c + -13 = 13.674794331 Reorder the terms: -13 + c = 13.674794331 Solving -13 + c = 13.674794331 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + c = 13.674794331 + 13 Combine like terms: -13 + 13 = 0 0 + c = 13.674794331 + 13 c = 13.674794331 + 13 Combine like terms: 13.674794331 + 13 = 26.674794331 c = 26.674794331 Simplifying c = 26.674794331Subproblem 2
c + -13 = -13.674794331 Simplifying c + -13 = -13.674794331 Reorder the terms: -13 + c = -13.674794331 Solving -13 + c = -13.674794331 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + c = -13.674794331 + 13 Combine like terms: -13 + 13 = 0 0 + c = -13.674794331 + 13 c = -13.674794331 + 13 Combine like terms: -13.674794331 + 13 = -0.674794331 c = -0.674794331 Simplifying c = -0.674794331Solution
The solution to the problem is based on the solutions from the subproblems. c = {26.674794331, -0.674794331}
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