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Simplifying 4c2 + -9c + -3 = 0 Reorder the terms: -3 + -9c + 4c2 = 0 Solving -3 + -9c + 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'. -0.75 + -2.25c + c2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.25c + 0.75 + c2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.25c + c2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.25c + c2 = 0 + 0.75 -2.25c + c2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.25c + c2 = 0.75 The c term is -2.25c. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25c + 1.265625 + c2 = 0.75 + 1.265625 Reorder the terms: 1.265625 + -2.25c + c2 = 0.75 + 1.265625 Combine like terms: 0.75 + 1.265625 = 2.015625 1.265625 + -2.25c + c2 = 2.015625 Factor a perfect square on the left side: (c + -1.125)(c + -1.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (c + -1.125) equal to 1.419727086 and -1.419727086.Subproblem 1
c + -1.125 = 1.419727086 Simplifying c + -1.125 = 1.419727086 Reorder the terms: -1.125 + c = 1.419727086 Solving -1.125 + c = 1.419727086 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + c = 1.419727086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + c = 1.419727086 + 1.125 c = 1.419727086 + 1.125 Combine like terms: 1.419727086 + 1.125 = 2.544727086 c = 2.544727086 Simplifying c = 2.544727086Subproblem 2
c + -1.125 = -1.419727086 Simplifying c + -1.125 = -1.419727086 Reorder the terms: -1.125 + c = -1.419727086 Solving -1.125 + c = -1.419727086 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + c = -1.419727086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + c = -1.419727086 + 1.125 c = -1.419727086 + 1.125 Combine like terms: -1.419727086 + 1.125 = -0.294727086 c = -0.294727086 Simplifying c = -0.294727086Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.544727086, -0.294727086}
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