x^2+1.3x-7.7=0

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Solution for x^2+1.3x-7.7=0 equation: 


Simplifying
x2 + 1.3x + -7.7 = 0

Reorder the terms:
-7.7 + 1.3x + x2 = 0

Solving
-7.7 + 1.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.7' to each side of the equation.
-7.7 + 1.3x + 7.7 + x2 = 0 + 7.7

Reorder the terms:
-7.7 + 7.7 + 1.3x + x2 = 0 + 7.7

Combine like terms: -7.7 + 7.7 = 0.0
0.0 + 1.3x + x2 = 0 + 7.7
1.3x + x2 = 0 + 7.7

Combine like terms: 0 + 7.7 = 7.7
1.3x + x2 = 7.7

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 7.7 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 7.7 + 0.4225

Combine like terms: 7.7 + 0.4225 = 8.1225
0.4225 + 1.3x + x2 = 8.1225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 8.1225

Calculate the square root of the right side: 2.85

Break this problem into two subproblems by setting 
(x + 0.65) equal to 2.85 and -2.85.


Subproblem 1
x + 0.65 = 2.85

Simplifying
x + 0.65 = 2.85

Reorder the terms:
0.65 + x = 2.85

Solving
0.65 + x = 2.85

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 2.85 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 2.85 + -0.65
x = 2.85 + -0.65

Combine like terms: 2.85 + -0.65 = 2.2
x = 2.2

Simplifying
x = 2.2


Subproblem 2
x + 0.65 = -2.85

Simplifying
x + 0.65 = -2.85

Reorder the terms:
0.65 + x = -2.85

Solving
0.65 + x = -2.85

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -2.85 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -2.85 + -0.65
x = -2.85 + -0.65

Combine like terms: -2.85 + -0.65 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2, -3.5}

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