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Simplifying c * c = 4c + 13 Multiply c * c c2 = 4c + 13 Reorder the terms: c2 = 13 + 4c Solving c2 = 13 + 4c Solving for variable 'c'. Reorder the terms: -13 + -4c + c2 = 13 + 4c + -13 + -4c Reorder the terms: -13 + -4c + c2 = 13 + -13 + 4c + -4c Combine like terms: 13 + -13 = 0 -13 + -4c + c2 = 0 + 4c + -4c -13 + -4c + c2 = 4c + -4c Combine like terms: 4c + -4c = 0 -13 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4c + 13 + c2 = 0 + 13 Reorder the terms: -13 + 13 + -4c + c2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4c + c2 = 0 + 13 -4c + c2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4c + c2 = 13 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = 13 + 4 Reorder the terms: 4 + -4c + c2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4c + c2 = 17 Factor a perfect square on the left side: (c + -2)(c + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (c + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
c + -2 = 4.123105626 Simplifying c + -2 = 4.123105626 Reorder the terms: -2 + c = 4.123105626 Solving -2 + c = 4.123105626 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + c = 4.123105626 + 2 c = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 c = 6.123105626 Simplifying c = 6.123105626Subproblem 2
c + -2 = -4.123105626 Simplifying c + -2 = -4.123105626 Reorder the terms: -2 + c = -4.123105626 Solving -2 + c = -4.123105626 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + c = -4.123105626 + 2 c = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 c = -2.123105626 Simplifying c = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.123105626, -2.123105626}
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