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Simplifying (2c2 + 6c + 4) + (5c2 + -7) = 0 Reorder the terms: (4 + 6c + 2c2) + (5c2 + -7) = 0 Remove parenthesis around (4 + 6c + 2c2) 4 + 6c + 2c2 + (5c2 + -7) = 0 Reorder the terms: 4 + 6c + 2c2 + (-7 + 5c2) = 0 Remove parenthesis around (-7 + 5c2) 4 + 6c + 2c2 + -7 + 5c2 = 0 Reorder the terms: 4 + -7 + 6c + 2c2 + 5c2 = 0 Combine like terms: 4 + -7 = -3 -3 + 6c + 2c2 + 5c2 = 0 Combine like terms: 2c2 + 5c2 = 7c2 -3 + 6c + 7c2 = 0 Solving -3 + 6c + 7c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 0.8571428571c + c2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.8571428571c + 0.4285714286 + c2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.8571428571c + c2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.8571428571c + c2 = 0 + 0.4285714286 0.8571428571c + c2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.8571428571c + c2 = 0.4285714286 The c term is 0.8571428571c. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571c + 0.1836734694 + c2 = 0.4285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571c + c2 = 0.4285714286 + 0.1836734694 Combine like terms: 0.4285714286 + 0.1836734694 = 0.612244898 0.1836734694 + 0.8571428571c + c2 = 0.612244898 Factor a perfect square on the left side: (c + 0.4285714286)(c + 0.4285714286) = 0.612244898 Calculate the square root of the right side: 0.782460796 Break this problem into two subproblems by setting (c + 0.4285714286) equal to 0.782460796 and -0.782460796.Subproblem 1
c + 0.4285714286 = 0.782460796 Simplifying c + 0.4285714286 = 0.782460796 Reorder the terms: 0.4285714286 + c = 0.782460796 Solving 0.4285714286 + c = 0.782460796 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + c = 0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + c = 0.782460796 + -0.4285714286 c = 0.782460796 + -0.4285714286 Combine like terms: 0.782460796 + -0.4285714286 = 0.3538893674 c = 0.3538893674 Simplifying c = 0.3538893674Subproblem 2
c + 0.4285714286 = -0.782460796 Simplifying c + 0.4285714286 = -0.782460796 Reorder the terms: 0.4285714286 + c = -0.782460796 Solving 0.4285714286 + c = -0.782460796 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + c = -0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + c = -0.782460796 + -0.4285714286 c = -0.782460796 + -0.4285714286 Combine like terms: -0.782460796 + -0.4285714286 = -1.2110322246 c = -1.2110322246 Simplifying c = -1.2110322246Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.3538893674, -1.2110322246}
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