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Simplifying c2 + -3c + -85 = 0 Reorder the terms: -85 + -3c + c2 = 0 Solving -85 + -3c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -3c + 85 + c2 = 0 + 85 Reorder the terms: -85 + 85 + -3c + c2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -3c + c2 = 0 + 85 -3c + c2 = 0 + 85 Combine like terms: 0 + 85 = 85 -3c + c2 = 85 The c term is -3c. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3c + 2.25 + c2 = 85 + 2.25 Reorder the terms: 2.25 + -3c + c2 = 85 + 2.25 Combine like terms: 85 + 2.25 = 87.25 2.25 + -3c + c2 = 87.25 Factor a perfect square on the left side: (c + -1.5)(c + -1.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (c + -1.5) equal to 9.340770846 and -9.340770846.Subproblem 1
c + -1.5 = 9.340770846 Simplifying c + -1.5 = 9.340770846 Reorder the terms: -1.5 + c = 9.340770846 Solving -1.5 + c = 9.340770846 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + c = 9.340770846 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = 9.340770846 + 1.5 c = 9.340770846 + 1.5 Combine like terms: 9.340770846 + 1.5 = 10.840770846 c = 10.840770846 Simplifying c = 10.840770846Subproblem 2
c + -1.5 = -9.340770846 Simplifying c + -1.5 = -9.340770846 Reorder the terms: -1.5 + c = -9.340770846 Solving -1.5 + c = -9.340770846 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + c = -9.340770846 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = -9.340770846 + 1.5 c = -9.340770846 + 1.5 Combine like terms: -9.340770846 + 1.5 = -7.840770846 c = -7.840770846 Simplifying c = -7.840770846Solution
The solution to the problem is based on the solutions from the subproblems. c = {10.840770846, -7.840770846}
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