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Simplifying c(c + -5) = 2(c + -5) + c Reorder the terms: c(-5 + c) = 2(c + -5) + c (-5 * c + c * c) = 2(c + -5) + c (-5c + c2) = 2(c + -5) + c Reorder the terms: -5c + c2 = 2(-5 + c) + c -5c + c2 = (-5 * 2 + c * 2) + c -5c + c2 = (-10 + 2c) + c Combine like terms: 2c + c = 3c -5c + c2 = -10 + 3c Solving -5c + c2 = -10 + 3c Solving for variable 'c'. Reorder the terms: 10 + -5c + -3c + c2 = -10 + 3c + 10 + -3c Combine like terms: -5c + -3c = -8c 10 + -8c + c2 = -10 + 3c + 10 + -3c Reorder the terms: 10 + -8c + c2 = -10 + 10 + 3c + -3c Combine like terms: -10 + 10 = 0 10 + -8c + c2 = 0 + 3c + -3c 10 + -8c + c2 = 3c + -3c Combine like terms: 3c + -3c = 0 10 + -8c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8c + -10 + c2 = 0 + -10 Reorder the terms: 10 + -10 + -8c + c2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8c + c2 = 0 + -10 -8c + c2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8c + c2 = -10 The c term is -8c. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8c + 16 + c2 = -10 + 16 Reorder the terms: 16 + -8c + c2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8c + c2 = 6 Factor a perfect square on the left side: (c + -4)(c + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (c + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
c + -4 = 2.449489743 Simplifying c + -4 = 2.449489743 Reorder the terms: -4 + c = 2.449489743 Solving -4 + c = 2.449489743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + c = 2.449489743 + 4 c = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 c = 6.449489743 Simplifying c = 6.449489743Subproblem 2
c + -4 = -2.449489743 Simplifying c + -4 = -2.449489743 Reorder the terms: -4 + c = -2.449489743 Solving -4 + c = -2.449489743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + c = -2.449489743 + 4 c = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 c = 1.550510257 Simplifying c = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.449489743, 1.550510257}
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