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Simplifying 7c3(8c2 + 2c + -9) = 0 Reorder the terms: 7c3(-9 + 2c + 8c2) = 0 (-9 * 7c3 + 2c * 7c3 + 8c2 * 7c3) = 0 (-63c3 + 14c4 + 56c5) = 0 Solving -63c3 + 14c4 + 56c5 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '7c3'. 7c3(-9 + 2c + 8c2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'c3' equal to zero and attempt to solve: Simplifying c3 = 0 Solving c3 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-9 + 2c + 8c2)' equal to zero and attempt to solve: Simplifying -9 + 2c + 8c2 = 0 Solving -9 + 2c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 0.25c + c2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.25c + 1.125 + c2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.25c + c2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.25c + c2 = 0 + 1.125 0.25c + c2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.25c + c2 = 1.125 The c term is 0.25c. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25c + 0.015625 + c2 = 1.125 + 0.015625 Reorder the terms: 0.015625 + 0.25c + c2 = 1.125 + 0.015625 Combine like terms: 1.125 + 0.015625 = 1.140625 0.015625 + 0.25c + c2 = 1.140625 Factor a perfect square on the left side: (c + 0.125)(c + 0.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (c + 0.125) equal to 1.068000468 and -1.068000468.Subproblem 1
c + 0.125 = 1.068000468 Simplifying c + 0.125 = 1.068000468 Reorder the terms: 0.125 + c = 1.068000468 Solving 0.125 + c = 1.068000468 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + c = 1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + c = 1.068000468 + -0.125 c = 1.068000468 + -0.125 Combine like terms: 1.068000468 + -0.125 = 0.943000468 c = 0.943000468 Simplifying c = 0.943000468Subproblem 2
c + 0.125 = -1.068000468 Simplifying c + 0.125 = -1.068000468 Reorder the terms: 0.125 + c = -1.068000468 Solving 0.125 + c = -1.068000468 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + c = -1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + c = -1.068000468 + -0.125 c = -1.068000468 + -0.125 Combine like terms: -1.068000468 + -0.125 = -1.193000468 c = -1.193000468 Simplifying c = -1.193000468Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.943000468, -1.193000468}Solution
c = {0.943000468, -1.193000468}
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