x^2+0.9x-7.92=0

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Solution for x^2+0.9x-7.92=0 equation: 


Simplifying
x2 + 0.9x + -7.92 = 0

Reorder the terms:
-7.92 + 0.9x + x2 = 0

Solving
-7.92 + 0.9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.92' to each side of the equation.
-7.92 + 0.9x + 7.92 + x2 = 0 + 7.92

Reorder the terms:
-7.92 + 7.92 + 0.9x + x2 = 0 + 7.92

Combine like terms: -7.92 + 7.92 = 0.00
0.00 + 0.9x + x2 = 0 + 7.92
0.9x + x2 = 0 + 7.92

Combine like terms: 0 + 7.92 = 7.92
0.9x + x2 = 7.92

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 7.92 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 7.92 + 0.2025

Combine like terms: 7.92 + 0.2025 = 8.1225
0.2025 + 0.9x + x2 = 8.1225

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 8.1225

Calculate the square root of the right side: 2.85

Break this problem into two subproblems by setting 
(x + 0.45) equal to 2.85 and -2.85.


Subproblem 1
x + 0.45 = 2.85

Simplifying
x + 0.45 = 2.85

Reorder the terms:
0.45 + x = 2.85

Solving
0.45 + x = 2.85

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x = 2.85 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x = 2.85 + -0.45
x = 2.85 + -0.45

Combine like terms: 2.85 + -0.45 = 2.4
x = 2.4

Simplifying
x = 2.4


Subproblem 2
x + 0.45 = -2.85

Simplifying
x + 0.45 = -2.85

Reorder the terms:
0.45 + x = -2.85

Solving
0.45 + x = -2.85

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x = -2.85 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x = -2.85 + -0.45
x = -2.85 + -0.45

Combine like terms: -2.85 + -0.45 = -3.3
x = -3.3

Simplifying
x = -3.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4, -3.3}

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