3x^4-7x^3-2x^2=0

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Solution for 3x^4-7x^3-2x^2=0 equation:


Simplifying
3x4 + -7x3 + -2x2 = 0

Reorder the terms:
-2x2 + -7x3 + 3x4 = 0

Solving
-2x2 + -7x3 + 3x4 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(-2 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + -7x + 3x2 = 0 Solving -2 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2.333333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2.333333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2.333333333x + x2 = 0 + 0.6666666667 -2.333333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2.333333333x + x2 = 0.6666666667 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 = 0.6666666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 0.6666666667 + 1.361111112 Combine like terms: 0.6666666667 + 1.361111112 = 2.0277777787 1.361111112 + -2.333333333x + x2 = 2.0277777787 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 2.0277777787 Calculate the square root of the right side: 1.424000625 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.424000625 and -1.424000625.

Subproblem 1

x + -1.166666667 = 1.424000625 Simplifying x + -1.166666667 = 1.424000625 Reorder the terms: -1.166666667 + x = 1.424000625 Solving -1.166666667 + x = 1.424000625 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 = 1.424000625 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.424000625 + 1.166666667 x = 1.424000625 + 1.166666667 Combine like terms: 1.424000625 + 1.166666667 = 2.590667292 x = 2.590667292 Simplifying x = 2.590667292

Subproblem 2

x + -1.166666667 = -1.424000625 Simplifying x + -1.166666667 = -1.424000625 Reorder the terms: -1.166666667 + x = -1.424000625 Solving -1.166666667 + x = -1.424000625 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 = -1.424000625 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.424000625 + 1.166666667 x = -1.424000625 + 1.166666667 Combine like terms: -1.424000625 + 1.166666667 = -0.257333958 x = -0.257333958 Simplifying x = -0.257333958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.590667292, -0.257333958}

Solution

x = {0, 2.590667292, -0.257333958}

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