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Simplifying c(2c + 3) + c + -3(7 + 4c) = 0 Reorder the terms: c(3 + 2c) + c + -3(7 + 4c) = 0 (3 * c + 2c * c) + c + -3(7 + 4c) = 0 (3c + 2c2) + c + -3(7 + 4c) = 0 3c + 2c2 + c + (7 * -3 + 4c * -3) = 0 3c + 2c2 + c + (-21 + -12c) = 0 Reorder the terms: -21 + 3c + c + -12c + 2c2 = 0 Combine like terms: 3c + c = 4c -21 + 4c + -12c + 2c2 = 0 Combine like terms: 4c + -12c = -8c -21 + -8c + 2c2 = 0 Solving -21 + -8c + 2c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -4c + c2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -4c + 10.5 + c2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -4c + c2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -4c + c2 = 0 + 10.5 -4c + c2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -4c + c2 = 10.5 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 = 10.5 + 4 Reorder the terms: 4 + -4c + c2 = 10.5 + 4 Combine like terms: 10.5 + 4 = 14.5 4 + -4c + c2 = 14.5 Factor a perfect square on the left side: (c + -2)(c + -2) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (c + -2) equal to 3.807886553 and -3.807886553.Subproblem 1
c + -2 = 3.807886553 Simplifying c + -2 = 3.807886553 Reorder the terms: -2 + c = 3.807886553 Solving -2 + c = 3.807886553 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 = 3.807886553 + 2 Combine like terms: -2 + 2 = 0 0 + c = 3.807886553 + 2 c = 3.807886553 + 2 Combine like terms: 3.807886553 + 2 = 5.807886553 c = 5.807886553 Simplifying c = 5.807886553Subproblem 2
c + -2 = -3.807886553 Simplifying c + -2 = -3.807886553 Reorder the terms: -2 + c = -3.807886553 Solving -2 + c = -3.807886553 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 = -3.807886553 + 2 Combine like terms: -2 + 2 = 0 0 + c = -3.807886553 + 2 c = -3.807886553 + 2 Combine like terms: -3.807886553 + 2 = -1.807886553 c = -1.807886553 Simplifying c = -1.807886553Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.807886553, -1.807886553}
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