2X^4=22X^3+56X^2

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Solution for 2X^4=22X^3+56X^2 equation:


Simplifying
2X4 = 22X3 + 56X2

Reorder the terms:
2X4 = 56X2 + 22X3

Solving
2X4 = 56X2 + 22X3

Solving for variable 'X'.

Reorder the terms:
-56X2 + -22X3 + 2X4 = 56X2 + 22X3 + -56X2 + -22X3

Reorder the terms:
-56X2 + -22X3 + 2X4 = 56X2 + -56X2 + 22X3 + -22X3

Combine like terms: 56X2 + -56X2 = 0
-56X2 + -22X3 + 2X4 = 0 + 22X3 + -22X3
-56X2 + -22X3 + 2X4 = 22X3 + -22X3

Combine like terms: 22X3 + -22X3 = 0
-56X2 + -22X3 + 2X4 = 0

Factor out the Greatest Common Factor (GCF), '2X2'.
2X2(-28 + -11X + X2) = 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 '(-28 + -11X + X2)' equal to zero and attempt to solve: Simplifying -28 + -11X + X2 = 0 Solving -28 + -11X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -11X + 28 + X2 = 0 + 28 Reorder the terms: -28 + 28 + -11X + X2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -11X + X2 = 0 + 28 -11X + X2 = 0 + 28 Combine like terms: 0 + 28 = 28 -11X + X2 = 28 The X term is -11X. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11X + 30.25 + X2 = 28 + 30.25 Reorder the terms: 30.25 + -11X + X2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + -11X + X2 = 58.25 Factor a perfect square on the left side: (X + -5.5)(X + -5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (X + -5.5) equal to 7.632168761 and -7.632168761.

Subproblem 1

X + -5.5 = 7.632168761 Simplifying X + -5.5 = 7.632168761 Reorder the terms: -5.5 + X = 7.632168761 Solving -5.5 + X = 7.632168761 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = 7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = 7.632168761 + 5.5 X = 7.632168761 + 5.5 Combine like terms: 7.632168761 + 5.5 = 13.132168761 X = 13.132168761 Simplifying X = 13.132168761

Subproblem 2

X + -5.5 = -7.632168761 Simplifying X + -5.5 = -7.632168761 Reorder the terms: -5.5 + X = -7.632168761 Solving -5.5 + X = -7.632168761 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = -7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = -7.632168761 + 5.5 X = -7.632168761 + 5.5 Combine like terms: -7.632168761 + 5.5 = -2.132168761 X = -2.132168761 Simplifying X = -2.132168761

Solution

The solution to the problem is based on the solutions from the subproblems. X = {13.132168761, -2.132168761}

Solution

X = {0, 13.132168761, -2.132168761}

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