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Simplifying 2c2 + 18c + -144 = 0 Reorder the terms: -144 + 18c + 2c2 = 0 Solving -144 + 18c + 2c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 9c + c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + 9c + c2)' equal to zero and attempt to solve: Simplifying -72 + 9c + c2 = 0 Solving -72 + 9c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 9c + 72 + c2 = 0 + 72 Reorder the terms: -72 + 72 + 9c + c2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 9c + c2 = 0 + 72 9c + c2 = 0 + 72 Combine like terms: 0 + 72 = 72 9c + c2 = 72 The c term is 9c. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9c + 20.25 + c2 = 72 + 20.25 Reorder the terms: 20.25 + 9c + c2 = 72 + 20.25 Combine like terms: 72 + 20.25 = 92.25 20.25 + 9c + c2 = 92.25 Factor a perfect square on the left side: (c + 4.5)(c + 4.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (c + 4.5) equal to 9.604686356 and -9.604686356.Subproblem 1
c + 4.5 = 9.604686356 Simplifying c + 4.5 = 9.604686356 Reorder the terms: 4.5 + c = 9.604686356 Solving 4.5 + c = 9.604686356 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = 9.604686356 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = 9.604686356 + -4.5 c = 9.604686356 + -4.5 Combine like terms: 9.604686356 + -4.5 = 5.104686356 c = 5.104686356 Simplifying c = 5.104686356Subproblem 2
c + 4.5 = -9.604686356 Simplifying c + 4.5 = -9.604686356 Reorder the terms: 4.5 + c = -9.604686356 Solving 4.5 + c = -9.604686356 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = -9.604686356 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = -9.604686356 + -4.5 c = -9.604686356 + -4.5 Combine like terms: -9.604686356 + -4.5 = -14.104686356 c = -14.104686356 Simplifying c = -14.104686356Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.104686356, -14.104686356}Solution
c = {5.104686356, -14.104686356}
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