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Simplifying c2 + 14c + -13 = 0 Reorder the terms: -13 + 14c + c2 = 0 Solving -13 + 14c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 14c + 13 + c2 = 0 + 13 Reorder the terms: -13 + 13 + 14c + c2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 14c + c2 = 0 + 13 14c + c2 = 0 + 13 Combine like terms: 0 + 13 = 13 14c + c2 = 13 The c term is 14c. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14c + 49 + c2 = 13 + 49 Reorder the terms: 49 + 14c + c2 = 13 + 49 Combine like terms: 13 + 49 = 62 49 + 14c + c2 = 62 Factor a perfect square on the left side: (c + 7)(c + 7) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (c + 7) equal to 7.874007874 and -7.874007874.Subproblem 1
c + 7 = 7.874007874 Simplifying c + 7 = 7.874007874 Reorder the terms: 7 + c = 7.874007874 Solving 7 + c = 7.874007874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + c = 7.874007874 + -7 Combine like terms: 7 + -7 = 0 0 + c = 7.874007874 + -7 c = 7.874007874 + -7 Combine like terms: 7.874007874 + -7 = 0.874007874 c = 0.874007874 Simplifying c = 0.874007874Subproblem 2
c + 7 = -7.874007874 Simplifying c + 7 = -7.874007874 Reorder the terms: 7 + c = -7.874007874 Solving 7 + c = -7.874007874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + c = -7.874007874 + -7 Combine like terms: 7 + -7 = 0 0 + c = -7.874007874 + -7 c = -7.874007874 + -7 Combine like terms: -7.874007874 + -7 = -14.874007874 c = -14.874007874 Simplifying c = -14.874007874Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.874007874, -14.874007874}
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