-0.69x^2-5.79x+6.2=0

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Solution for -0.69x^2-5.79x+6.2=0 equation: 


Simplifying
-0.69x2 + -5.79x + 6.2 = 0

Reorder the terms:
6.2 + -5.79x + -0.69x2 = 0

Solving
6.2 + -5.79x + -0.69x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.69 the coefficient of the squared term: 

Divide each side by '-0.69'.
-8.985507246 + 8.391304348x + x2 = 0

Move the constant term to the right:

Add '8.985507246' to each side of the equation.
-8.985507246 + 8.391304348x + 8.985507246 + x2 = 0 + 8.985507246

Reorder the terms:
-8.985507246 + 8.985507246 + 8.391304348x + x2 = 0 + 8.985507246

Combine like terms: -8.985507246 + 8.985507246 = 0.000000000
0.000000000 + 8.391304348x + x2 = 0 + 8.985507246
8.391304348x + x2 = 0 + 8.985507246

Combine like terms: 0 + 8.985507246 = 8.985507246
8.391304348x + x2 = 8.985507246

The x term is 8.391304348x.  Take half its coefficient (4.195652174).
Square it (17.60349717) and add it to both sides.

Add '17.60349717' to each side of the equation.
8.391304348x + 17.60349717 + x2 = 8.985507246 + 17.60349717

Reorder the terms:
17.60349717 + 8.391304348x + x2 = 8.985507246 + 17.60349717

Combine like terms: 8.985507246 + 17.60349717 = 26.589004416
17.60349717 + 8.391304348x + x2 = 26.589004416

Factor a perfect square on the left side:
(x + 4.195652174)(x + 4.195652174) = 26.589004416

Calculate the square root of the right side: 5.156452697

Break this problem into two subproblems by setting 
(x + 4.195652174) equal to 5.156452697 and -5.156452697.


Subproblem 1
x + 4.195652174 = 5.156452697

Simplifying
x + 4.195652174 = 5.156452697

Reorder the terms:
4.195652174 + x = 5.156452697

Solving
4.195652174 + x = 5.156452697

Solving for variable 'x'.

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

Add '-4.195652174' to each side of the equation.
4.195652174 + -4.195652174 + x = 5.156452697 + -4.195652174

Combine like terms: 4.195652174 + -4.195652174 = 0.000000000
0.000000000 + x = 5.156452697 + -4.195652174
x = 5.156452697 + -4.195652174

Combine like terms: 5.156452697 + -4.195652174 = 0.960800523
x = 0.960800523

Simplifying
x = 0.960800523


Subproblem 2
x + 4.195652174 = -5.156452697

Simplifying
x + 4.195652174 = -5.156452697

Reorder the terms:
4.195652174 + x = -5.156452697

Solving
4.195652174 + x = -5.156452697

Solving for variable 'x'.

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

Add '-4.195652174' to each side of the equation.
4.195652174 + -4.195652174 + x = -5.156452697 + -4.195652174

Combine like terms: 4.195652174 + -4.195652174 = 0.000000000
0.000000000 + x = -5.156452697 + -4.195652174
x = -5.156452697 + -4.195652174

Combine like terms: -5.156452697 + -4.195652174 = -9.352104871
x = -9.352104871

Simplifying
x = -9.352104871


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.960800523, -9.352104871}

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