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Simplifying 5c2 + 7c + 5 = 6 Reorder the terms: 5 + 7c + 5c2 = 6 Solving 5 + 7c + 5c2 = 6 Solving for variable 'c'. Reorder the terms: 5 + -6 + 7c + 5c2 = 6 + -6 Combine like terms: 5 + -6 = -1 -1 + 7c + 5c2 = 6 + -6 Combine like terms: 6 + -6 = 0 -1 + 7c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 1.4c + c2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.4c + 0.2 + c2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.4c + c2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.4c + c2 = 0 + 0.2 1.4c + c2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.4c + c2 = 0.2 The c term is 1.4c. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4c + 0.49 + c2 = 0.2 + 0.49 Reorder the terms: 0.49 + 1.4c + c2 = 0.2 + 0.49 Combine like terms: 0.2 + 0.49 = 0.69 0.49 + 1.4c + c2 = 0.69 Factor a perfect square on the left side: (c + 0.7)(c + 0.7) = 0.69 Calculate the square root of the right side: 0.830662386 Break this problem into two subproblems by setting (c + 0.7) equal to 0.830662386 and -0.830662386.Subproblem 1
c + 0.7 = 0.830662386 Simplifying c + 0.7 = 0.830662386 Reorder the terms: 0.7 + c = 0.830662386 Solving 0.7 + c = 0.830662386 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + c = 0.830662386 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + c = 0.830662386 + -0.7 c = 0.830662386 + -0.7 Combine like terms: 0.830662386 + -0.7 = 0.130662386 c = 0.130662386 Simplifying c = 0.130662386Subproblem 2
c + 0.7 = -0.830662386 Simplifying c + 0.7 = -0.830662386 Reorder the terms: 0.7 + c = -0.830662386 Solving 0.7 + c = -0.830662386 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + c = -0.830662386 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + c = -0.830662386 + -0.7 c = -0.830662386 + -0.7 Combine like terms: -0.830662386 + -0.7 = -1.530662386 c = -1.530662386 Simplifying c = -1.530662386Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.130662386, -1.530662386}
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