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Simplifying -1c2 + -3c + 2 = 0 Reorder the terms: 2 + -3c + -1c2 = 0 Solving 2 + -3c + -1c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 3c + c2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3c + 2 + c2 = 0 + 2 Reorder the terms: -2 + 2 + 3c + c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3c + c2 = 0 + 2 3c + c2 = 0 + 2 Combine like terms: 0 + 2 = 2 3c + c2 = 2 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 = 2 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3c + c2 = 4.25 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (c + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
c + 1.5 = 2.061552813 Simplifying c + 1.5 = 2.061552813 Reorder the terms: 1.5 + c = 2.061552813 Solving 1.5 + c = 2.061552813 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 = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 2.061552813 + -1.5 c = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 c = 0.561552813 Simplifying c = 0.561552813Subproblem 2
c + 1.5 = -2.061552813 Simplifying c + 1.5 = -2.061552813 Reorder the terms: 1.5 + c = -2.061552813 Solving 1.5 + c = -2.061552813 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 = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -2.061552813 + -1.5 c = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 c = -3.561552813 Simplifying c = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.561552813, -3.561552813}
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