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Simplifying 5 = c2 + 8c Reorder the terms: 5 = 8c + c2 Solving 5 = 8c + c2 Solving for variable 'c'. Reorder the terms: 5 + -8c + -1c2 = 8c + -8c + c2 + -1c2 Combine like terms: 8c + -8c = 0 5 + -8c + -1c2 = 0 + c2 + -1c2 5 + -8c + -1c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 5 + -8c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 8c + c2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 8c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + 8c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 8c + c2 = 0 + 5 8c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 8c + c2 = 5 The c term is 8c. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8c + 16 + c2 = 5 + 16 Reorder the terms: 16 + 8c + c2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + 8c + c2 = 21 Factor a perfect square on the left side: (c + 4)(c + 4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (c + 4) equal to 4.582575695 and -4.582575695.Subproblem 1
c + 4 = 4.582575695 Simplifying c + 4 = 4.582575695 Reorder the terms: 4 + c = 4.582575695 Solving 4 + c = 4.582575695 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + c = 4.582575695 + -4 c = 4.582575695 + -4 Combine like terms: 4.582575695 + -4 = 0.582575695 c = 0.582575695 Simplifying c = 0.582575695Subproblem 2
c + 4 = -4.582575695 Simplifying c + 4 = -4.582575695 Reorder the terms: 4 + c = -4.582575695 Solving 4 + c = -4.582575695 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + c = -4.582575695 + -4 c = -4.582575695 + -4 Combine like terms: -4.582575695 + -4 = -8.582575695 c = -8.582575695 Simplifying c = -8.582575695Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.582575695, -8.582575695}
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