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Simplifying 2 + 5c = 2c(c + -2) Reorder the terms: 2 + 5c = 2c(-2 + c) 2 + 5c = (-2 * 2c + c * 2c) 2 + 5c = (-4c + 2c2) Solving 2 + 5c = -4c + 2c2 Solving for variable 'c'. Combine like terms: 5c + 4c = 9c 2 + 9c + -2c2 = -4c + 2c2 + 4c + -2c2 Reorder the terms: 2 + 9c + -2c2 = -4c + 4c + 2c2 + -2c2 Combine like terms: -4c + 4c = 0 2 + 9c + -2c2 = 0 + 2c2 + -2c2 2 + 9c + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 2 + 9c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -4.5c + c2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.5c + 1 + c2 = 0 + 1 Reorder the terms: -1 + 1 + -4.5c + c2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.5c + c2 = 0 + 1 -4.5c + c2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.5c + c2 = 1 The c term is -4.5c. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5c + 5.0625 + c2 = 1 + 5.0625 Reorder the terms: 5.0625 + -4.5c + c2 = 1 + 5.0625 Combine like terms: 1 + 5.0625 = 6.0625 5.0625 + -4.5c + c2 = 6.0625 Factor a perfect square on the left side: (c + -2.25)(c + -2.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (c + -2.25) equal to 2.46221445 and -2.46221445.Subproblem 1
c + -2.25 = 2.46221445 Simplifying c + -2.25 = 2.46221445 Reorder the terms: -2.25 + c = 2.46221445 Solving -2.25 + c = 2.46221445 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = 2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = 2.46221445 + 2.25 c = 2.46221445 + 2.25 Combine like terms: 2.46221445 + 2.25 = 4.71221445 c = 4.71221445 Simplifying c = 4.71221445Subproblem 2
c + -2.25 = -2.46221445 Simplifying c + -2.25 = -2.46221445 Reorder the terms: -2.25 + c = -2.46221445 Solving -2.25 + c = -2.46221445 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = -2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = -2.46221445 + 2.25 c = -2.46221445 + 2.25 Combine like terms: -2.46221445 + 2.25 = -0.21221445 c = -0.21221445 Simplifying c = -0.21221445Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.71221445, -0.21221445}
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