10x^2-18x^3+14x^4=

Solution for 10x^2-18x^3+14x^4= equation:

Simplifying
10x2 + -18x3 + 14x4 = 0

Solving
10x2 + -18x3 + 14x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(5 + -9x + 7x2) = 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 '(5 + -9x + 7x2)' equal to zero and attempt to solve:

Simplifying
5 + -9x + 7x2 = 0

Solving
5 + -9x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.7142857143 + -1.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -1.285714286x + -0.7142857143 + x2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -1.285714286x + x2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -1.285714286x + x2 = 0 + -0.7142857143
-1.285714286x + x2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-1.285714286x + x2 = -0.7142857143

The x term is -1.285714286x.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286x + 0.4132653063 + x2 = -0.7142857143 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286x + x2 = -0.7142857143 + 0.4132653063

Combine like terms: -0.7142857143 + 0.4132653063 = -0.301020408
0.4132653063 + -1.285714286x + x2 = -0.301020408

Factor a perfect square on the left side:
(x + -0.642857143)(x + -0.642857143) = -0.301020408

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}