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Simplifying 15c2 + -51c + -30 = 9c + 15 Reorder the terms: -30 + -51c + 15c2 = 9c + 15 Reorder the terms: -30 + -51c + 15c2 = 15 + 9c Solving -30 + -51c + 15c2 = 15 + 9c Solving for variable 'c'. Reorder the terms: -30 + -15 + -51c + -9c + 15c2 = 15 + 9c + -15 + -9c Combine like terms: -30 + -15 = -45 -45 + -51c + -9c + 15c2 = 15 + 9c + -15 + -9c Combine like terms: -51c + -9c = -60c -45 + -60c + 15c2 = 15 + 9c + -15 + -9c Reorder the terms: -45 + -60c + 15c2 = 15 + -15 + 9c + -9c Combine like terms: 15 + -15 = 0 -45 + -60c + 15c2 = 0 + 9c + -9c -45 + -60c + 15c2 = 9c + -9c Combine like terms: 9c + -9c = 0 -45 + -60c + 15c2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-3 + -4c + c2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-3 + -4c + c2)' equal to zero and attempt to solve: Simplifying -3 + -4c + c2 = 0 Solving -3 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -4c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + -4c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4c + c2 = 0 + 3 -4c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4c + c2 = 3 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = 3 + 4 Reorder the terms: 4 + -4c + c2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4c + c2 = 7 Factor a perfect square on the left side: (c + -2)(c + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (c + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
c + -2 = 2.645751311 Simplifying c + -2 = 2.645751311 Reorder the terms: -2 + c = 2.645751311 Solving -2 + c = 2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + c = 2.645751311 + 2 c = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 c = 4.645751311 Simplifying c = 4.645751311Subproblem 2
c + -2 = -2.645751311 Simplifying c + -2 = -2.645751311 Reorder the terms: -2 + c = -2.645751311 Solving -2 + c = -2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + c = -2.645751311 + 2 c = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 c = -0.645751311 Simplifying c = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.645751311, -0.645751311}Solution
c = {4.645751311, -0.645751311}
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