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Simplifying 4c2 + -10c + -180 = 0 Reorder the terms: -180 + -10c + 4c2 = 0 Solving -180 + -10c + 4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -5c + 2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -5c + 2c2)' equal to zero and attempt to solve: Simplifying -90 + -5c + 2c2 = 0 Solving -90 + -5c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45 + -2.5c + c2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -2.5c + 45 + c2 = 0 + 45 Reorder the terms: -45 + 45 + -2.5c + c2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -2.5c + c2 = 0 + 45 -2.5c + c2 = 0 + 45 Combine like terms: 0 + 45 = 45 -2.5c + c2 = 45 The c term is -2.5c. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5c + 1.5625 + c2 = 45 + 1.5625 Reorder the terms: 1.5625 + -2.5c + c2 = 45 + 1.5625 Combine like terms: 45 + 1.5625 = 46.5625 1.5625 + -2.5c + c2 = 46.5625 Factor a perfect square on the left side: (c + -1.25)(c + -1.25) = 46.5625 Calculate the square root of the right side: 6.823672032 Break this problem into two subproblems by setting (c + -1.25) equal to 6.823672032 and -6.823672032.Subproblem 1
c + -1.25 = 6.823672032 Simplifying c + -1.25 = 6.823672032 Reorder the terms: -1.25 + c = 6.823672032 Solving -1.25 + c = 6.823672032 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + c = 6.823672032 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + c = 6.823672032 + 1.25 c = 6.823672032 + 1.25 Combine like terms: 6.823672032 + 1.25 = 8.073672032 c = 8.073672032 Simplifying c = 8.073672032Subproblem 2
c + -1.25 = -6.823672032 Simplifying c + -1.25 = -6.823672032 Reorder the terms: -1.25 + c = -6.823672032 Solving -1.25 + c = -6.823672032 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + c = -6.823672032 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + c = -6.823672032 + 1.25 c = -6.823672032 + 1.25 Combine like terms: -6.823672032 + 1.25 = -5.573672032 c = -5.573672032 Simplifying c = -5.573672032Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.073672032, -5.573672032}Solution
c = {8.073672032, -5.573672032}
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