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Simplifying c2 + 22c + -3 = 0 Reorder the terms: -3 + 22c + c2 = 0 Solving -3 + 22c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 22c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + 22c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 22c + c2 = 0 + 3 22c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 22c + c2 = 3 The c term is 22c. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22c + 121 + c2 = 3 + 121 Reorder the terms: 121 + 22c + c2 = 3 + 121 Combine like terms: 3 + 121 = 124 121 + 22c + c2 = 124 Factor a perfect square on the left side: (c + 11)(c + 11) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (c + 11) equal to 11.135528726 and -11.135528726.Subproblem 1
c + 11 = 11.135528726 Simplifying c + 11 = 11.135528726 Reorder the terms: 11 + c = 11.135528726 Solving 11 + c = 11.135528726 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + c = 11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + c = 11.135528726 + -11 c = 11.135528726 + -11 Combine like terms: 11.135528726 + -11 = 0.135528726 c = 0.135528726 Simplifying c = 0.135528726Subproblem 2
c + 11 = -11.135528726 Simplifying c + 11 = -11.135528726 Reorder the terms: 11 + c = -11.135528726 Solving 11 + c = -11.135528726 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + c = -11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + c = -11.135528726 + -11 c = -11.135528726 + -11 Combine like terms: -11.135528726 + -11 = -22.135528726 c = -22.135528726 Simplifying c = -22.135528726Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.135528726, -22.135528726}
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