2x^4+6x^3+14x^2=

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Solution for 2x^4+6x^3+14x^2= equation: 


Simplifying
2x4 + 6x3 + 14x2 = 0

Reorder the terms:
14x2 + 6x3 + 2x4 = 0

Solving
14x2 + 6x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(7 + 3x + 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 '(7 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 3x + x2 = 0

Solving
7 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 3x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 3x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x + x2 = 0 + -7
3x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
3x + x2 = -7

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -7 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -7 + 2.25

Combine like terms: -7 + 2.25 = -4.75
2.25 + 3x + x2 = -4.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -4.75

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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