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Simplifying (4c2 + 6c + -7) + (c2 + c) = 0 Reorder the terms: (-7 + 6c + 4c2) + (c2 + c) = 0 Remove parenthesis around (-7 + 6c + 4c2) -7 + 6c + 4c2 + (c2 + c) = 0 Reorder the terms: -7 + 6c + 4c2 + (c + c2) = 0 Remove parenthesis around (c + c2) -7 + 6c + 4c2 + c + c2 = 0 Reorder the terms: -7 + 6c + c + 4c2 + c2 = 0 Combine like terms: 6c + c = 7c -7 + 7c + 4c2 + c2 = 0 Combine like terms: 4c2 + c2 = 5c2 -7 + 7c + 5c2 = 0 Solving -7 + 7c + 5c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 1.4c + c2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 1.4c + 1.4 + c2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 1.4c + c2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 1.4c + c2 = 0 + 1.4 1.4c + c2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 1.4c + c2 = 1.4 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 = 1.4 + 0.49 Reorder the terms: 0.49 + 1.4c + c2 = 1.4 + 0.49 Combine like terms: 1.4 + 0.49 = 1.89 0.49 + 1.4c + c2 = 1.89 Factor a perfect square on the left side: (c + 0.7)(c + 0.7) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (c + 0.7) equal to 1.374772708 and -1.374772708.Subproblem 1
c + 0.7 = 1.374772708 Simplifying c + 0.7 = 1.374772708 Reorder the terms: 0.7 + c = 1.374772708 Solving 0.7 + c = 1.374772708 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 = 1.374772708 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + c = 1.374772708 + -0.7 c = 1.374772708 + -0.7 Combine like terms: 1.374772708 + -0.7 = 0.674772708 c = 0.674772708 Simplifying c = 0.674772708Subproblem 2
c + 0.7 = -1.374772708 Simplifying c + 0.7 = -1.374772708 Reorder the terms: 0.7 + c = -1.374772708 Solving 0.7 + c = -1.374772708 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 = -1.374772708 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + c = -1.374772708 + -0.7 c = -1.374772708 + -0.7 Combine like terms: -1.374772708 + -0.7 = -2.074772708 c = -2.074772708 Simplifying c = -2.074772708Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.674772708, -2.074772708}
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