2.7x^2+0.5x-7=0

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Solution for 2.7x^2+0.5x-7=0 equation: 


Simplifying
2.7x2 + 0.5x + -7 = 0

Reorder the terms:
-7 + 0.5x + 2.7x2 = 0

Solving
-7 + 0.5x + 2.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.7'.
-2.592592593 + 0.1851851852x + x2 = 0

Move the constant term to the right:

Add '2.592592593' to each side of the equation.
-2.592592593 + 0.1851851852x + 2.592592593 + x2 = 0 + 2.592592593

Reorder the terms:
-2.592592593 + 2.592592593 + 0.1851851852x + x2 = 0 + 2.592592593

Combine like terms: -2.592592593 + 2.592592593 = 0.000000000
0.000000000 + 0.1851851852x + x2 = 0 + 2.592592593
0.1851851852x + x2 = 0 + 2.592592593

Combine like terms: 0 + 2.592592593 = 2.592592593
0.1851851852x + x2 = 2.592592593

The x term is 0.1851851852x.  Take half its coefficient (0.0925925926).
Square it (0.008573388204) and add it to both sides.

Add '0.008573388204' to each side of the equation.
0.1851851852x + 0.008573388204 + x2 = 2.592592593 + 0.008573388204

Reorder the terms:
0.008573388204 + 0.1851851852x + x2 = 2.592592593 + 0.008573388204

Combine like terms: 2.592592593 + 0.008573388204 = 2.601165981204
0.008573388204 + 0.1851851852x + x2 = 2.601165981204

Factor a perfect square on the left side:
(x + 0.0925925926)(x + 0.0925925926) = 2.601165981204

Calculate the square root of the right side: 1.612813065

Break this problem into two subproblems by setting 
(x + 0.0925925926) equal to 1.612813065 and -1.612813065.


Subproblem 1
x + 0.0925925926 = 1.612813065

Simplifying
x + 0.0925925926 = 1.612813065

Reorder the terms:
0.0925925926 + x = 1.612813065

Solving
0.0925925926 + x = 1.612813065

Solving for variable 'x'.

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

Add '-0.0925925926' to each side of the equation.
0.0925925926 + -0.0925925926 + x = 1.612813065 + -0.0925925926

Combine like terms: 0.0925925926 + -0.0925925926 = 0.0000000000
0.0000000000 + x = 1.612813065 + -0.0925925926
x = 1.612813065 + -0.0925925926

Combine like terms: 1.612813065 + -0.0925925926 = 1.5202204724
x = 1.5202204724

Simplifying
x = 1.5202204724


Subproblem 2
x + 0.0925925926 = -1.612813065

Simplifying
x + 0.0925925926 = -1.612813065

Reorder the terms:
0.0925925926 + x = -1.612813065

Solving
0.0925925926 + x = -1.612813065

Solving for variable 'x'.

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

Add '-0.0925925926' to each side of the equation.
0.0925925926 + -0.0925925926 + x = -1.612813065 + -0.0925925926

Combine like terms: 0.0925925926 + -0.0925925926 = 0.0000000000
0.0000000000 + x = -1.612813065 + -0.0925925926
x = -1.612813065 + -0.0925925926

Combine like terms: -1.612813065 + -0.0925925926 = -1.7054056576
x = -1.7054056576

Simplifying
x = -1.7054056576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5202204724, -1.7054056576}

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