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Simplifying 4c2 + c + -1200 = 0 Reorder the terms: -1200 + c + 4c2 = 0 Solving -1200 + c + 4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -300 + 0.25c + c2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 0.25c + 300 + c2 = 0 + 300 Reorder the terms: -300 + 300 + 0.25c + c2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 0.25c + c2 = 0 + 300 0.25c + c2 = 0 + 300 Combine like terms: 0 + 300 = 300 0.25c + c2 = 300 The c term is c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25c + 0.25 + c2 = 300 + 0.25 Reorder the terms: 0.25 + 0.25c + c2 = 300 + 0.25 Combine like terms: 300 + 0.25 = 300.25 0.25 + 0.25c + c2 = 300.25 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (c + 0.5) equal to 17.327723451 and -17.327723451.Subproblem 1
c + 0.5 = 17.327723451 Simplifying c + 0.5 = 17.327723451 Reorder the terms: 0.5 + c = 17.327723451 Solving 0.5 + c = 17.327723451 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 17.327723451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 17.327723451 + -0.5 c = 17.327723451 + -0.5 Combine like terms: 17.327723451 + -0.5 = 16.827723451 c = 16.827723451 Simplifying c = 16.827723451Subproblem 2
c + 0.5 = -17.327723451 Simplifying c + 0.5 = -17.327723451 Reorder the terms: 0.5 + c = -17.327723451 Solving 0.5 + c = -17.327723451 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = -17.327723451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -17.327723451 + -0.5 c = -17.327723451 + -0.5 Combine like terms: -17.327723451 + -0.5 = -17.827723451 c = -17.827723451 Simplifying c = -17.827723451Solution
The solution to the problem is based on the solutions from the subproblems. c = {16.827723451, -17.827723451}
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