4x^4-6x^3-2x^2=0

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Solution for 4x^4-6x^3-2x^2=0 equation:


Simplifying
4x4 + -6x3 + -2x2 = 0

Reorder the terms:
-2x2 + -6x3 + 4x4 = 0

Solving
-2x2 + -6x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-1 + -3x + 2x2) = 0

Ignore the factor 2.

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 '(-1 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -3x + 2x2 = 0 Solving -1 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.5x + x2 = 0 + 0.5 -1.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.5x + x2 = 0.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.5 + 0.5625 Combine like terms: 0.5 + 0.5625 = 1.0625 0.5625 + -1.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -0.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -0.75 = 1.030776406 Simplifying x + -0.75 = 1.030776406 Reorder the terms: -0.75 + x = 1.030776406 Solving -0.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.030776406 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.030776406 + 0.75 x = 1.030776406 + 0.75 Combine like terms: 1.030776406 + 0.75 = 1.780776406 x = 1.780776406 Simplifying x = 1.780776406

Subproblem 2

x + -0.75 = -1.030776406 Simplifying x + -0.75 = -1.030776406 Reorder the terms: -0.75 + x = -1.030776406 Solving -0.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.030776406 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.030776406 + 0.75 x = -1.030776406 + 0.75 Combine like terms: -1.030776406 + 0.75 = -0.280776406 x = -0.280776406 Simplifying x = -0.280776406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.780776406, -0.280776406}

Solution

x = {0, 1.780776406, -0.280776406}

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