4c^3-16c^2-28c=0

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Solution for 4c^3-16c^2-28c=0 equation:


Simplifying
4c3 + -16c2 + -28c = 0

Reorder the terms:
-28c + -16c2 + 4c3 = 0

Solving
-28c + -16c2 + 4c3 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '4c'.
4c(-7 + -4c + c2) = 0

Ignore the factor 4.

Subproblem 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 = 0

Subproblem 2

Set the factor '(-7 + -4c + c2)' equal to zero and attempt to solve: Simplifying -7 + -4c + c2 = 0 Solving -7 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -4c + 7 + c2 = 0 + 7 Reorder the terms: -7 + 7 + -4c + c2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4c + c2 = 0 + 7 -4c + c2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4c + c2 = 7 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 = 7 + 4 Reorder the terms: 4 + -4c + c2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4c + c2 = 11 Factor a perfect square on the left side: (c + -2)(c + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (c + -2) equal to 3.31662479 and -3.31662479.

Subproblem 1

c + -2 = 3.31662479 Simplifying c + -2 = 3.31662479 Reorder the terms: -2 + c = 3.31662479 Solving -2 + c = 3.31662479 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 = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + c = 3.31662479 + 2 c = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 c = 5.31662479 Simplifying c = 5.31662479

Subproblem 2

c + -2 = -3.31662479 Simplifying c + -2 = -3.31662479 Reorder the terms: -2 + c = -3.31662479 Solving -2 + c = -3.31662479 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 = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + c = -3.31662479 + 2 c = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 c = -1.31662479 Simplifying c = -1.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. c = {5.31662479, -1.31662479}

Solution

c = {0, 5.31662479, -1.31662479}

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