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Simplifying 4c3 + 25c2 + -28c = 0 Reorder the terms: -28c + 25c2 + 4c3 = 0 Solving -28c + 25c2 + 4c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(-28 + 25c + 4c2) = 0Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(-28 + 25c + 4c2)' equal to zero and attempt to solve: Simplifying -28 + 25c + 4c2 = 0 Solving -28 + 25c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + 6.25c + c2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 6.25c + 7 + c2 = 0 + 7 Reorder the terms: -7 + 7 + 6.25c + c2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 6.25c + c2 = 0 + 7 6.25c + c2 = 0 + 7 Combine like terms: 0 + 7 = 7 6.25c + c2 = 7 The c term is 6.25c. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25c + 9.765625 + c2 = 7 + 9.765625 Reorder the terms: 9.765625 + 6.25c + c2 = 7 + 9.765625 Combine like terms: 7 + 9.765625 = 16.765625 9.765625 + 6.25c + c2 = 16.765625 Factor a perfect square on the left side: (c + 3.125)(c + 3.125) = 16.765625 Calculate the square root of the right side: 4.094584839 Break this problem into two subproblems by setting (c + 3.125) equal to 4.094584839 and -4.094584839.Subproblem 1
c + 3.125 = 4.094584839 Simplifying c + 3.125 = 4.094584839 Reorder the terms: 3.125 + c = 4.094584839 Solving 3.125 + c = 4.094584839 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + c = 4.094584839 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + c = 4.094584839 + -3.125 c = 4.094584839 + -3.125 Combine like terms: 4.094584839 + -3.125 = 0.969584839 c = 0.969584839 Simplifying c = 0.969584839Subproblem 2
c + 3.125 = -4.094584839 Simplifying c + 3.125 = -4.094584839 Reorder the terms: 3.125 + c = -4.094584839 Solving 3.125 + c = -4.094584839 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + c = -4.094584839 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + c = -4.094584839 + -3.125 c = -4.094584839 + -3.125 Combine like terms: -4.094584839 + -3.125 = -7.219584839 c = -7.219584839 Simplifying c = -7.219584839Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.969584839, -7.219584839}Solution
c = {0, 0.969584839, -7.219584839}
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