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Simplifying 2c2 + -176c + 192 = 0 Reorder the terms: 192 + -176c + 2c2 = 0 Solving 192 + -176c + 2c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(96 + -88c + c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(96 + -88c + c2)' equal to zero and attempt to solve: Simplifying 96 + -88c + c2 = 0 Solving 96 + -88c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -88c + -96 + c2 = 0 + -96 Reorder the terms: 96 + -96 + -88c + c2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -88c + c2 = 0 + -96 -88c + c2 = 0 + -96 Combine like terms: 0 + -96 = -96 -88c + c2 = -96 The c term is -88c. Take half its coefficient (-44). Square it (1936) and add it to both sides. Add '1936' to each side of the equation. -88c + 1936 + c2 = -96 + 1936 Reorder the terms: 1936 + -88c + c2 = -96 + 1936 Combine like terms: -96 + 1936 = 1840 1936 + -88c + c2 = 1840 Factor a perfect square on the left side: (c + -44)(c + -44) = 1840 Calculate the square root of the right side: 42.895221179 Break this problem into two subproblems by setting (c + -44) equal to 42.895221179 and -42.895221179.Subproblem 1
c + -44 = 42.895221179 Simplifying c + -44 = 42.895221179 Reorder the terms: -44 + c = 42.895221179 Solving -44 + c = 42.895221179 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '44' to each side of the equation. -44 + 44 + c = 42.895221179 + 44 Combine like terms: -44 + 44 = 0 0 + c = 42.895221179 + 44 c = 42.895221179 + 44 Combine like terms: 42.895221179 + 44 = 86.895221179 c = 86.895221179 Simplifying c = 86.895221179Subproblem 2
c + -44 = -42.895221179 Simplifying c + -44 = -42.895221179 Reorder the terms: -44 + c = -42.895221179 Solving -44 + c = -42.895221179 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '44' to each side of the equation. -44 + 44 + c = -42.895221179 + 44 Combine like terms: -44 + 44 = 0 0 + c = -42.895221179 + 44 c = -42.895221179 + 44 Combine like terms: -42.895221179 + 44 = 1.104778821 c = 1.104778821 Simplifying c = 1.104778821Solution
The solution to the problem is based on the solutions from the subproblems. c = {86.895221179, 1.104778821}Solution
c = {86.895221179, 1.104778821}
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