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Simplifying c2 + -14c + -7 = 0 Reorder the terms: -7 + -14c + c2 = 0 Solving -7 + -14c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -14c + 7 + c2 = 0 + 7 Reorder the terms: -7 + 7 + -14c + c2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -14c + c2 = 0 + 7 -14c + c2 = 0 + 7 Combine like terms: 0 + 7 = 7 -14c + c2 = 7 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 = 7 + 49 Reorder the terms: 49 + -14c + c2 = 7 + 49 Combine like terms: 7 + 49 = 56 49 + -14c + c2 = 56 Factor a perfect square on the left side: (c + -7)(c + -7) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (c + -7) equal to 7.483314774 and -7.483314774.Subproblem 1
c + -7 = 7.483314774 Simplifying c + -7 = 7.483314774 Reorder the terms: -7 + c = 7.483314774 Solving -7 + c = 7.483314774 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 = 7.483314774 + 7 Combine like terms: -7 + 7 = 0 0 + c = 7.483314774 + 7 c = 7.483314774 + 7 Combine like terms: 7.483314774 + 7 = 14.483314774 c = 14.483314774 Simplifying c = 14.483314774Subproblem 2
c + -7 = -7.483314774 Simplifying c + -7 = -7.483314774 Reorder the terms: -7 + c = -7.483314774 Solving -7 + c = -7.483314774 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 = -7.483314774 + 7 Combine like terms: -7 + 7 = 0 0 + c = -7.483314774 + 7 c = -7.483314774 + 7 Combine like terms: -7.483314774 + 7 = -0.483314774 c = -0.483314774 Simplifying c = -0.483314774Solution
The solution to the problem is based on the solutions from the subproblems. c = {14.483314774, -0.483314774}
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