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Simplifying 13c2 + -134c + -2 = 0 Reorder the terms: -2 + -134c + 13c2 = 0 Solving -2 + -134c + 13c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.1538461538 + -10.30769231c + c2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + -10.30769231c + 0.1538461538 + c2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + -10.30769231c + c2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + -10.30769231c + c2 = 0 + 0.1538461538 -10.30769231c + c2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 -10.30769231c + c2 = 0.1538461538 The c term is -10.30769231c. Take half its coefficient (-5.153846155). Square it (26.56213019) and add it to both sides. Add '26.56213019' to each side of the equation. -10.30769231c + 26.56213019 + c2 = 0.1538461538 + 26.56213019 Reorder the terms: 26.56213019 + -10.30769231c + c2 = 0.1538461538 + 26.56213019 Combine like terms: 0.1538461538 + 26.56213019 = 26.7159763438 26.56213019 + -10.30769231c + c2 = 26.7159763438 Factor a perfect square on the left side: (c + -5.153846155)(c + -5.153846155) = 26.7159763438 Calculate the square root of the right side: 5.168749979 Break this problem into two subproblems by setting (c + -5.153846155) equal to 5.168749979 and -5.168749979.Subproblem 1
c + -5.153846155 = 5.168749979 Simplifying c + -5.153846155 = 5.168749979 Reorder the terms: -5.153846155 + c = 5.168749979 Solving -5.153846155 + c = 5.168749979 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5.153846155' to each side of the equation. -5.153846155 + 5.153846155 + c = 5.168749979 + 5.153846155 Combine like terms: -5.153846155 + 5.153846155 = 0.000000000 0.000000000 + c = 5.168749979 + 5.153846155 c = 5.168749979 + 5.153846155 Combine like terms: 5.168749979 + 5.153846155 = 10.322596134 c = 10.322596134 Simplifying c = 10.322596134Subproblem 2
c + -5.153846155 = -5.168749979 Simplifying c + -5.153846155 = -5.168749979 Reorder the terms: -5.153846155 + c = -5.168749979 Solving -5.153846155 + c = -5.168749979 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5.153846155' to each side of the equation. -5.153846155 + 5.153846155 + c = -5.168749979 + 5.153846155 Combine like terms: -5.153846155 + 5.153846155 = 0.000000000 0.000000000 + c = -5.168749979 + 5.153846155 c = -5.168749979 + 5.153846155 Combine like terms: -5.168749979 + 5.153846155 = -0.014903824 c = -0.014903824 Simplifying c = -0.014903824Solution
The solution to the problem is based on the solutions from the subproblems. c = {10.322596134, -0.014903824}
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