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Simplifying 4c4 + 18c2 + -4 = 0 Reorder the terms: -4 + 18c2 + 4c4 = 0 Solving -4 + 18c2 + 4c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 9c2 + 2c4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 9c2 + 2c4)' equal to zero and attempt to solve: Simplifying -2 + 9c2 + 2c4 = 0 Solving -2 + 9c2 + 2c4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 4.5c2 + c4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4.5c2 + 1 + c4 = 0 + 1 Reorder the terms: -1 + 1 + 4.5c2 + c4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4.5c2 + c4 = 0 + 1 4.5c2 + c4 = 0 + 1 Combine like terms: 0 + 1 = 1 4.5c2 + c4 = 1 The c term is 4.5c2. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5c2 + 5.0625 + c4 = 1 + 5.0625 Reorder the terms: 5.0625 + 4.5c2 + c4 = 1 + 5.0625 Combine like terms: 1 + 5.0625 = 6.0625 5.0625 + 4.5c2 + c4 = 6.0625 Factor a perfect square on the left side: (c2 + 2.25)(c2 + 2.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (c2 + 2.25) equal to 2.46221445 and -2.46221445.Subproblem 1
c2 + 2.25 = 2.46221445 Simplifying c2 + 2.25 = 2.46221445 Reorder the terms: 2.25 + c2 = 2.46221445 Solving 2.25 + c2 = 2.46221445 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + c2 = 2.46221445 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + c2 = 2.46221445 + -2.25 c2 = 2.46221445 + -2.25 Combine like terms: 2.46221445 + -2.25 = 0.21221445 c2 = 0.21221445 Simplifying c2 = 0.21221445 Take the square root of each side: c = {-0.460667396, 0.460667396}Subproblem 2
c2 + 2.25 = -2.46221445 Simplifying c2 + 2.25 = -2.46221445 Reorder the terms: 2.25 + c2 = -2.46221445 Solving 2.25 + c2 = -2.46221445 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + c2 = -2.46221445 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + c2 = -2.46221445 + -2.25 c2 = -2.46221445 + -2.25 Combine like terms: -2.46221445 + -2.25 = -4.71221445 c2 = -4.71221445 Simplifying c2 = -4.71221445 Reorder the terms: 4.71221445 + c2 = -4.71221445 + 4.71221445 Combine like terms: -4.71221445 + 4.71221445 = 0.00000000 4.71221445 + c2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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