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

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


Simplifying
0 = -4x4 + 3x3 + -2x2

Reorder the terms:
0 = -2x2 + 3x3 + -4x4

Solving
0 = -2x2 + 3x3 + -4x4

Solving for variable 'x'.
Remove the zero:
2x2 + -3x3 + 4x4 = -2x2 + 3x3 + -4x4 + 2x2 + -3x3 + 4x4

Reorder the terms:
2x2 + -3x3 + 4x4 = -2x2 + 2x2 + 3x3 + -3x3 + -4x4 + 4x4

Combine like terms: -2x2 + 2x2 = 0
2x2 + -3x3 + 4x4 = 0 + 3x3 + -3x3 + -4x4 + 4x4
2x2 + -3x3 + 4x4 = 3x3 + -3x3 + -4x4 + 4x4

Combine like terms: 3x3 + -3x3 = 0
2x2 + -3x3 + 4x4 = 0 + -4x4 + 4x4
2x2 + -3x3 + 4x4 = -4x4 + 4x4

Combine like terms: -4x4 + 4x4 = 0
2x2 + -3x3 + 4x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(2 + -3x + 4x2) = 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 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + -3x + 4x2 = 0 Solving 2 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.75x + x2 = 0 + -0.5 -0.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.75x + x2 = -0.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.5 + 0.140625 Combine like terms: -0.5 + 0.140625 = -0.359375 0.140625 + -0.75x + x2 = -0.359375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.359375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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