0=x^3-14x^2-13x

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Solution for 0=x^3-14x^2-13x equation:


Simplifying
0 = x3 + -14x2 + -13x

Reorder the terms:
0 = -13x + -14x2 + x3

Solving
0 = -13x + -14x2 + x3

Solving for variable 'x'.
Remove the zero:
13x + 14x2 + -1x3 = -13x + -14x2 + x3 + 13x + 14x2 + -1x3

Reorder the terms:
13x + 14x2 + -1x3 = -13x + 13x + -14x2 + 14x2 + x3 + -1x3

Combine like terms: -13x + 13x = 0
13x + 14x2 + -1x3 = 0 + -14x2 + 14x2 + x3 + -1x3
13x + 14x2 + -1x3 = -14x2 + 14x2 + x3 + -1x3

Combine like terms: -14x2 + 14x2 = 0
13x + 14x2 + -1x3 = 0 + x3 + -1x3
13x + 14x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
13x + 14x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + 14x + -1x2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(13 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying 13 + 14x + -1x2 = 0 Solving 13 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -14x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -14x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -14x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -14x + x2 = 0 + 13 -14x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -14x + x2 = 13 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 13 + 49 Reorder the terms: 49 + -14x + x2 = 13 + 49 Combine like terms: 13 + 49 = 62 49 + -14x + x2 = 62 Factor a perfect square on the left side: (x + -7)(x + -7) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + -7) equal to 7.874007874 and -7.874007874.

Subproblem 1

x + -7 = 7.874007874 Simplifying x + -7 = 7.874007874 Reorder the terms: -7 + x = 7.874007874 Solving -7 + x = 7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.874007874 + 7 x = 7.874007874 + 7 Combine like terms: 7.874007874 + 7 = 14.874007874 x = 14.874007874 Simplifying x = 14.874007874

Subproblem 2

x + -7 = -7.874007874 Simplifying x + -7 = -7.874007874 Reorder the terms: -7 + x = -7.874007874 Solving -7 + x = -7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.874007874 + 7 x = -7.874007874 + 7 Combine like terms: -7.874007874 + 7 = -0.874007874 x = -0.874007874 Simplifying x = -0.874007874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.874007874, -0.874007874}

Solution

x = {0, 14.874007874, -0.874007874}

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