6x^3-14x^2-16x=

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Solution for 6x^3-14x^2-16x= equation:


Simplifying
6x3 + -14x2 + -16x = 0

Reorder the terms:
-16x + -14x2 + 6x3 = 0

Solving
-16x + -14x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + -7x + 3x2) = 0

Ignore the factor 2.

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 '(-8 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -8 + -7x + 3x2 = 0 Solving -8 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -2.333333333x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -2.333333333x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + 2.666666667 -2.333333333x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -2.333333333x + x2 = 2.666666667 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 2.666666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 2.666666667 + 1.361111112 Combine like terms: 2.666666667 + 1.361111112 = 4.027777779 1.361111112 + -2.333333333x + x2 = 4.027777779 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 4.027777779 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + -1.166666667) equal to 2.00693243 and -2.00693243.

Subproblem 1

x + -1.166666667 = 2.00693243 Simplifying x + -1.166666667 = 2.00693243 Reorder the terms: -1.166666667 + x = 2.00693243 Solving -1.166666667 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 2.00693243 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 2.00693243 + 1.166666667 x = 2.00693243 + 1.166666667 Combine like terms: 2.00693243 + 1.166666667 = 3.173599097 x = 3.173599097 Simplifying x = 3.173599097

Subproblem 2

x + -1.166666667 = -2.00693243 Simplifying x + -1.166666667 = -2.00693243 Reorder the terms: -1.166666667 + x = -2.00693243 Solving -1.166666667 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -2.00693243 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -2.00693243 + 1.166666667 x = -2.00693243 + 1.166666667 Combine like terms: -2.00693243 + 1.166666667 = -0.840265763 x = -0.840265763 Simplifying x = -0.840265763

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.173599097, -0.840265763}

Solution

x = {0, 3.173599097, -0.840265763}

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