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Simplifying 5 + -2c(4 + c) = 0 5 + (4 * -2c + c * -2c) = 0 5 + (-8c + -2c2) = 0 Solving 5 + -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'. -2.5 + 4c + c2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 4c + 2.5 + c2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 4c + c2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 4c + c2 = 0 + 2.5 4c + c2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 4c + c2 = 2.5 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 = 2.5 + 4 Reorder the terms: 4 + 4c + c2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 4 + 4c + c2 = 6.5 Factor a perfect square on the left side: (c + 2)(c + 2) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (c + 2) equal to 2.549509757 and -2.549509757.Subproblem 1
c + 2 = 2.549509757 Simplifying c + 2 = 2.549509757 Reorder the terms: 2 + c = 2.549509757 Solving 2 + c = 2.549509757 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 = 2.549509757 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.549509757 + -2 c = 2.549509757 + -2 Combine like terms: 2.549509757 + -2 = 0.549509757 c = 0.549509757 Simplifying c = 0.549509757Subproblem 2
c + 2 = -2.549509757 Simplifying c + 2 = -2.549509757 Reorder the terms: 2 + c = -2.549509757 Solving 2 + c = -2.549509757 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 = -2.549509757 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.549509757 + -2 c = -2.549509757 + -2 Combine like terms: -2.549509757 + -2 = -4.549509757 c = -4.549509757 Simplifying c = -4.549509757Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.549509757, -4.549509757}
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