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Simplifying 4c2 + 6c + -3c2 + -2c + -3 = 0 Reorder the terms: -3 + 6c + -2c + 4c2 + -3c2 = 0 Combine like terms: 6c + -2c = 4c -3 + 4c + 4c2 + -3c2 = 0 Combine like terms: 4c2 + -3c2 = 1c2 -3 + 4c + 1c2 = 0 Solving -3 + 4c + 1c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + 4c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4c + c2 = 0 + 3 4c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 4c + c2 = 3 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = 3 + 4 Reorder the terms: 4 + 4c + c2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4c + c2 = 7 Factor a perfect square on the left side: (c + 2)(c + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (c + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
c + 2 = 2.645751311 Simplifying c + 2 = 2.645751311 Reorder the terms: 2 + c = 2.645751311 Solving 2 + c = 2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.645751311 + -2 c = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 c = 0.645751311 Simplifying c = 0.645751311Subproblem 2
c + 2 = -2.645751311 Simplifying c + 2 = -2.645751311 Reorder the terms: 2 + c = -2.645751311 Solving 2 + c = -2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.645751311 + -2 c = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 c = -4.645751311 Simplifying c = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.645751311, -4.645751311}
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