3a^4-5a^3+7a^2=

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Solution for 3a^4-5a^3+7a^2= equation: 


Simplifying
3a4 + -5a3 + 7a2 = 0

Reorder the terms:
7a2 + -5a3 + 3a4 = 0

Solving
7a2 + -5a3 + 3a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(7 + -5a + 3a2) = 0


Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a2 = 0

Take the square root of each side:
a = {0}

Subproblem 2
Set the factor '(7 + -5a + 3a2)' equal to zero and attempt to solve:

Simplifying
7 + -5a + 3a2 = 0

Solving
7 + -5a + 3a2 = 0

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

Divide each side by '3'.
2.333333333 + -1.666666667a + a2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -1.666666667a + -2.333333333 + a2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -1.666666667a + a2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -1.666666667a + a2 = 0 + -2.333333333
-1.666666667a + a2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-1.666666667a + a2 = -2.333333333

The a term is -1.666666667a.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667a + 0.6944444447 + a2 = -2.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667a + a2 = -2.333333333 + 0.6944444447

Combine like terms: -2.333333333 + 0.6944444447 = -1.6388888883
0.6944444447 + -1.666666667a + a2 = -1.6388888883

Factor a perfect square on the left side:
(a + -0.8333333335)(a + -0.8333333335) = -1.6388888883

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
a = {0}

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