3a^3=14a^2+25a

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Solution for 3a^3=14a^2+25a equation: 


Simplifying
3a3 = 14a2 + 25a

Reorder the terms:
3a3 = 25a + 14a2

Solving
3a3 = 25a + 14a2

Solving for variable 'a'.

Reorder the terms:
-25a + -14a2 + 3a3 = 25a + 14a2 + -25a + -14a2

Reorder the terms:
-25a + -14a2 + 3a3 = 25a + -25a + 14a2 + -14a2

Combine like terms: 25a + -25a = 0
-25a + -14a2 + 3a3 = 0 + 14a2 + -14a2
-25a + -14a2 + 3a3 = 14a2 + -14a2

Combine like terms: 14a2 + -14a2 = 0
-25a + -14a2 + 3a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-25 + -14a + 3a2) = 0


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(-25 + -14a + 3a2)' equal to zero and attempt to solve:

Simplifying
-25 + -14a + 3a2 = 0

Solving
-25 + -14a + 3a2 = 0

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

Divide each side by '3'.
-8.333333333 + -4.666666667a + a2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -4.666666667a + 8.333333333 + a2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -4.666666667a + a2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -4.666666667a + a2 = 0 + 8.333333333
-4.666666667a + a2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-4.666666667a + a2 = 8.333333333

The a term is -4.666666667a.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667a + 5.444444448 + a2 = 8.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667a + a2 = 8.333333333 + 5.444444448

Combine like terms: 8.333333333 + 5.444444448 = 13.777777781
5.444444448 + -4.666666667a + a2 = 13.777777781

Factor a perfect square on the left side:
(a + -2.333333334)(a + -2.333333334) = 13.777777781

Calculate the square root of the right side: 3.711842909

Break this problem into two subproblems by setting 
(a + -2.333333334) equal to 3.711842909 and -3.711842909.


Subproblem 1
a + -2.333333334 = 3.711842909

Simplifying
a + -2.333333334 = 3.711842909

Reorder the terms:
-2.333333334 + a = 3.711842909

Solving
-2.333333334 + a = 3.711842909

Solving for variable 'a'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + a = 3.711842909 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + a = 3.711842909 + 2.333333334
a = 3.711842909 + 2.333333334

Combine like terms: 3.711842909 + 2.333333334 = 6.045176243
a = 6.045176243

Simplifying
a = 6.045176243


Subproblem 2
a + -2.333333334 = -3.711842909

Simplifying
a + -2.333333334 = -3.711842909

Reorder the terms:
-2.333333334 + a = -3.711842909

Solving
-2.333333334 + a = -3.711842909

Solving for variable 'a'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + a = -3.711842909 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + a = -3.711842909 + 2.333333334
a = -3.711842909 + 2.333333334

Combine like terms: -3.711842909 + 2.333333334 = -1.378509575
a = -1.378509575

Simplifying
a = -1.378509575


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.045176243, -1.378509575}
Solution
a = {0, 6.045176243, -1.378509575}

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