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Simplifying 56c2 + -23c = 23 Reorder the terms: -23c + 56c2 = 23 Solving -23c + 56c2 = 23 Solving for variable 'c'. Reorder the terms: -23 + -23c + 56c2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -23c + 56c2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.4107142857 + -0.4107142857c + c2 = 0 Move the constant term to the right: Add '0.4107142857' to each side of the equation. -0.4107142857 + -0.4107142857c + 0.4107142857 + c2 = 0 + 0.4107142857 Reorder the terms: -0.4107142857 + 0.4107142857 + -0.4107142857c + c2 = 0 + 0.4107142857 Combine like terms: -0.4107142857 + 0.4107142857 = 0.0000000000 0.0000000000 + -0.4107142857c + c2 = 0 + 0.4107142857 -0.4107142857c + c2 = 0 + 0.4107142857 Combine like terms: 0 + 0.4107142857 = 0.4107142857 -0.4107142857c + c2 = 0.4107142857 The c term is -0.4107142857c. Take half its coefficient (-0.2053571429). Square it (0.04217155614) and add it to both sides. Add '0.04217155614' to each side of the equation. -0.4107142857c + 0.04217155614 + c2 = 0.4107142857 + 0.04217155614 Reorder the terms: 0.04217155614 + -0.4107142857c + c2 = 0.4107142857 + 0.04217155614 Combine like terms: 0.4107142857 + 0.04217155614 = 0.45288584184 0.04217155614 + -0.4107142857c + c2 = 0.45288584184 Factor a perfect square on the left side: (c + -0.2053571429)(c + -0.2053571429) = 0.45288584184 Calculate the square root of the right side: 0.672967935 Break this problem into two subproblems by setting (c + -0.2053571429) equal to 0.672967935 and -0.672967935.Subproblem 1
c + -0.2053571429 = 0.672967935 Simplifying c + -0.2053571429 = 0.672967935 Reorder the terms: -0.2053571429 + c = 0.672967935 Solving -0.2053571429 + c = 0.672967935 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2053571429' to each side of the equation. -0.2053571429 + 0.2053571429 + c = 0.672967935 + 0.2053571429 Combine like terms: -0.2053571429 + 0.2053571429 = 0.0000000000 0.0000000000 + c = 0.672967935 + 0.2053571429 c = 0.672967935 + 0.2053571429 Combine like terms: 0.672967935 + 0.2053571429 = 0.8783250779 c = 0.8783250779 Simplifying c = 0.8783250779Subproblem 2
c + -0.2053571429 = -0.672967935 Simplifying c + -0.2053571429 = -0.672967935 Reorder the terms: -0.2053571429 + c = -0.672967935 Solving -0.2053571429 + c = -0.672967935 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2053571429' to each side of the equation. -0.2053571429 + 0.2053571429 + c = -0.672967935 + 0.2053571429 Combine like terms: -0.2053571429 + 0.2053571429 = 0.0000000000 0.0000000000 + c = -0.672967935 + 0.2053571429 c = -0.672967935 + 0.2053571429 Combine like terms: -0.672967935 + 0.2053571429 = -0.4676107921 c = -0.4676107921 Simplifying c = -0.4676107921Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.8783250779, -0.4676107921}
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