3x^2+7.25x=2

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Solution for 3x^2+7.25x=2 equation:


Simplifying
3x2 + 7.25x = 2

Reorder the terms:
7.25x + 3x2 = 2

Solving
7.25x + 3x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 7.25x + 3x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 7.25x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + 2.416666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2.416666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2.416666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2.416666667x + x2 = 0 + 0.6666666667
2.416666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2.416666667x + x2 = 0.6666666667

The x term is 2.416666667x.  Take half its coefficient (1.208333334).
Square it (1.460069446) and add it to both sides.

Add '1.460069446' to each side of the equation.
2.416666667x + 1.460069446 + x2 = 0.6666666667 + 1.460069446

Reorder the terms:
1.460069446 + 2.416666667x + x2 = 0.6666666667 + 1.460069446

Combine like terms: 0.6666666667 + 1.460069446 = 2.1267361127
1.460069446 + 2.416666667x + x2 = 2.1267361127

Factor a perfect square on the left side:
(x + 1.208333334)(x + 1.208333334) = 2.1267361127

Calculate the square root of the right side: 1.458333334

Break this problem into two subproblems by setting 
(x + 1.208333334) equal to 1.458333334 and -1.458333334.


Subproblem 1
x + 1.208333334 = 1.458333334

Simplifying
x + 1.208333334 = 1.458333334

Reorder the terms:
1.208333334 + x = 1.458333334

Solving
1.208333334 + x = 1.458333334

Solving for variable 'x'.

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

Add '-1.208333334' to each side of the equation.
1.208333334 + -1.208333334 + x = 1.458333334 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + x = 1.458333334 + -1.208333334
x = 1.458333334 + -1.208333334

Combine like terms: 1.458333334 + -1.208333334 = 0.25
x = 0.25

Simplifying
x = 0.25


Subproblem 2
x + 1.208333334 = -1.458333334

Simplifying
x + 1.208333334 = -1.458333334

Reorder the terms:
1.208333334 + x = -1.458333334

Solving
1.208333334 + x = -1.458333334

Solving for variable 'x'.

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

Add '-1.208333334' to each side of the equation.
1.208333334 + -1.208333334 + x = -1.458333334 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + x = -1.458333334 + -1.208333334
x = -1.458333334 + -1.208333334

Combine like terms: -1.458333334 + -1.208333334 = -2.666666668
x = -2.666666668

Simplifying
x = -2.666666668


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.25, -2.666666668}

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