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Simplifying c2 + -14c + -2 = 0 Reorder the terms: -2 + -14c + c2 = 0 Solving -2 + -14c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -14c + 2 + c2 = 0 + 2 Reorder the terms: -2 + 2 + -14c + c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -14c + c2 = 0 + 2 -14c + c2 = 0 + 2 Combine like terms: 0 + 2 = 2 -14c + c2 = 2 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 = 2 + 49 Reorder the terms: 49 + -14c + c2 = 2 + 49 Combine like terms: 2 + 49 = 51 49 + -14c + c2 = 51 Factor a perfect square on the left side: (c + -7)(c + -7) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (c + -7) equal to 7.141428429 and -7.141428429.Subproblem 1
c + -7 = 7.141428429 Simplifying c + -7 = 7.141428429 Reorder the terms: -7 + c = 7.141428429 Solving -7 + c = 7.141428429 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 = 7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + c = 7.141428429 + 7 c = 7.141428429 + 7 Combine like terms: 7.141428429 + 7 = 14.141428429 c = 14.141428429 Simplifying c = 14.141428429Subproblem 2
c + -7 = -7.141428429 Simplifying c + -7 = -7.141428429 Reorder the terms: -7 + c = -7.141428429 Solving -7 + c = -7.141428429 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 = -7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + c = -7.141428429 + 7 c = -7.141428429 + 7 Combine like terms: -7.141428429 + 7 = -0.141428429 c = -0.141428429 Simplifying c = -0.141428429Solution
The solution to the problem is based on the solutions from the subproblems. c = {14.141428429, -0.141428429}
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