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Simplifying 25 + -1(2c + 4) = 2(c + 3) * c Reorder the terms: 25 + -1(4 + 2c) = 2(c + 3) * c 25 + (4 * -1 + 2c * -1) = 2(c + 3) * c 25 + (-4 + -2c) = 2(c + 3) * c Combine like terms: 25 + -4 = 21 21 + -2c = 2(c + 3) * c Reorder the terms: 21 + -2c = 2(3 + c) * c Reorder the terms for easier multiplication: 21 + -2c = 2c(3 + c) 21 + -2c = (3 * 2c + c * 2c) 21 + -2c = (6c + 2c2) Solving 21 + -2c = 6c + 2c2 Solving for variable 'c'. Combine like terms: -2c + -6c = -8c 21 + -8c + -2c2 = 6c + 2c2 + -6c + -2c2 Reorder the terms: 21 + -8c + -2c2 = 6c + -6c + 2c2 + -2c2 Combine like terms: 6c + -6c = 0 21 + -8c + -2c2 = 0 + 2c2 + -2c2 21 + -8c + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 21 + -8c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -10.5 + 4c + c2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 4c + 10.5 + c2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 4c + c2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 4c + c2 = 0 + 10.5 4c + c2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 4c + c2 = 10.5 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = 10.5 + 4 Reorder the terms: 4 + 4c + c2 = 10.5 + 4 Combine like terms: 10.5 + 4 = 14.5 4 + 4c + c2 = 14.5 Factor a perfect square on the left side: (c + 2)(c + 2) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (c + 2) equal to 3.807886553 and -3.807886553.Subproblem 1
c + 2 = 3.807886553 Simplifying c + 2 = 3.807886553 Reorder the terms: 2 + c = 3.807886553 Solving 2 + c = 3.807886553 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 3.807886553 + -2 Combine like terms: 2 + -2 = 0 0 + c = 3.807886553 + -2 c = 3.807886553 + -2 Combine like terms: 3.807886553 + -2 = 1.807886553 c = 1.807886553 Simplifying c = 1.807886553Subproblem 2
c + 2 = -3.807886553 Simplifying c + 2 = -3.807886553 Reorder the terms: 2 + c = -3.807886553 Solving 2 + c = -3.807886553 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -3.807886553 + -2 Combine like terms: 2 + -2 = 0 0 + c = -3.807886553 + -2 c = -3.807886553 + -2 Combine like terms: -3.807886553 + -2 = -5.807886553 c = -5.807886553 Simplifying c = -5.807886553Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.807886553, -5.807886553}
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