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Simplifying -7c + -5 = -7c2 + -3c + 8 Reorder the terms: -5 + -7c = -7c2 + -3c + 8 Reorder the terms: -5 + -7c = 8 + -3c + -7c2 Solving -5 + -7c = 8 + -3c + -7c2 Solving for variable 'c'. Reorder the terms: -5 + -8 + -7c + 3c + 7c2 = 8 + -3c + -7c2 + -8 + 3c + 7c2 Combine like terms: -5 + -8 = -13 -13 + -7c + 3c + 7c2 = 8 + -3c + -7c2 + -8 + 3c + 7c2 Combine like terms: -7c + 3c = -4c -13 + -4c + 7c2 = 8 + -3c + -7c2 + -8 + 3c + 7c2 Reorder the terms: -13 + -4c + 7c2 = 8 + -8 + -3c + 3c + -7c2 + 7c2 Combine like terms: 8 + -8 = 0 -13 + -4c + 7c2 = 0 + -3c + 3c + -7c2 + 7c2 -13 + -4c + 7c2 = -3c + 3c + -7c2 + 7c2 Combine like terms: -3c + 3c = 0 -13 + -4c + 7c2 = 0 + -7c2 + 7c2 -13 + -4c + 7c2 = -7c2 + 7c2 Combine like terms: -7c2 + 7c2 = 0 -13 + -4c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -0.5714285714c + c2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -0.5714285714c + 1.857142857 + c2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -0.5714285714c + c2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -0.5714285714c + c2 = 0 + 1.857142857 -0.5714285714c + c2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -0.5714285714c + c2 = 1.857142857 The c term is -0.5714285714c. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714c + 0.08163265305 + c2 = 1.857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714c + c2 = 1.857142857 + 0.08163265305 Combine like terms: 1.857142857 + 0.08163265305 = 1.93877551005 0.08163265305 + -0.5714285714c + c2 = 1.93877551005 Factor a perfect square on the left side: (c + -0.2857142857)(c + -0.2857142857) = 1.93877551005 Calculate the square root of the right side: 1.392399192 Break this problem into two subproblems by setting (c + -0.2857142857) equal to 1.392399192 and -1.392399192.Subproblem 1
c + -0.2857142857 = 1.392399192 Simplifying c + -0.2857142857 = 1.392399192 Reorder the terms: -0.2857142857 + c = 1.392399192 Solving -0.2857142857 + c = 1.392399192 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + c = 1.392399192 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + c = 1.392399192 + 0.2857142857 c = 1.392399192 + 0.2857142857 Combine like terms: 1.392399192 + 0.2857142857 = 1.6781134777 c = 1.6781134777 Simplifying c = 1.6781134777Subproblem 2
c + -0.2857142857 = -1.392399192 Simplifying c + -0.2857142857 = -1.392399192 Reorder the terms: -0.2857142857 + c = -1.392399192 Solving -0.2857142857 + c = -1.392399192 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + c = -1.392399192 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + c = -1.392399192 + 0.2857142857 c = -1.392399192 + 0.2857142857 Combine like terms: -1.392399192 + 0.2857142857 = -1.1066849063 c = -1.1066849063 Simplifying c = -1.1066849063Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.6781134777, -1.1066849063}
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