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Simplifying c2 + -3c + -14 = 0 Reorder the terms: -14 + -3c + c2 = 0 Solving -14 + -3c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -3c + 14 + c2 = 0 + 14 Reorder the terms: -14 + 14 + -3c + c2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3c + c2 = 0 + 14 -3c + c2 = 0 + 14 Combine like terms: 0 + 14 = 14 -3c + c2 = 14 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 = 14 + 2.25 Reorder the terms: 2.25 + -3c + c2 = 14 + 2.25 Combine like terms: 14 + 2.25 = 16.25 2.25 + -3c + c2 = 16.25 Factor a perfect square on the left side: (c + -1.5)(c + -1.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (c + -1.5) equal to 4.031128874 and -4.031128874.Subproblem 1
c + -1.5 = 4.031128874 Simplifying c + -1.5 = 4.031128874 Reorder the terms: -1.5 + c = 4.031128874 Solving -1.5 + c = 4.031128874 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 = 4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = 4.031128874 + 1.5 c = 4.031128874 + 1.5 Combine like terms: 4.031128874 + 1.5 = 5.531128874 c = 5.531128874 Simplifying c = 5.531128874Subproblem 2
c + -1.5 = -4.031128874 Simplifying c + -1.5 = -4.031128874 Reorder the terms: -1.5 + c = -4.031128874 Solving -1.5 + c = -4.031128874 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 = -4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = -4.031128874 + 1.5 c = -4.031128874 + 1.5 Combine like terms: -4.031128874 + 1.5 = -2.531128874 c = -2.531128874 Simplifying c = -2.531128874Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.531128874, -2.531128874}
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