3x^2+14x-27=0

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Solution for 3x^2+14x-27=0 equation: 


Simplifying
3x2 + 14x + -27 = 0

Reorder the terms:
-27 + 14x + 3x2 = 0

Solving
-27 + 14x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-9 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 4.666666667x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 4.666666667x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 4.666666667x + x2 = 0 + 9
4.666666667x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
4.666666667x + x2 = 9

The x term is 4.666666667x.  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.
4.666666667x + 5.444444448 + x2 = 9 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 9 + 5.444444448

Combine like terms: 9 + 5.444444448 = 14.444444448
5.444444448 + 4.666666667x + x2 = 14.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 14.444444448

Calculate the square root of the right side: 3.800584751

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 3.800584751 and -3.800584751.


Subproblem 1
x + 2.333333334 = 3.800584751

Simplifying
x + 2.333333334 = 3.800584751

Reorder the terms:
2.333333334 + x = 3.800584751

Solving
2.333333334 + x = 3.800584751

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 3.800584751 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 3.800584751 + -2.333333334
x = 3.800584751 + -2.333333334

Combine like terms: 3.800584751 + -2.333333334 = 1.467251417
x = 1.467251417

Simplifying
x = 1.467251417


Subproblem 2
x + 2.333333334 = -3.800584751

Simplifying
x + 2.333333334 = -3.800584751

Reorder the terms:
2.333333334 + x = -3.800584751

Solving
2.333333334 + x = -3.800584751

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -3.800584751 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -3.800584751 + -2.333333334
x = -3.800584751 + -2.333333334

Combine like terms: -3.800584751 + -2.333333334 = -6.133918085
x = -6.133918085

Simplifying
x = -6.133918085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.467251417, -6.133918085}

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