x=7.24-5-x^2

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Solution for x=7.24-5-x^2 equation: 


Simplifying
x = 7.24 + -5 + -1x2

Combine like terms: 7.24 + -5 = 2.24
x = 2.24 + -1x2

Solving
x = 2.24 + -1x2

Solving for variable 'x'.

Reorder the terms:
-2.24 + x + x2 = 2.24 + -1x2 + -2.24 + x2

Reorder the terms:
-2.24 + x + x2 = 2.24 + -2.24 + -1x2 + x2

Combine like terms: 2.24 + -2.24 = 0.00
-2.24 + x + x2 = 0.00 + -1x2 + x2
-2.24 + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2.24 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.24' to each side of the equation.
-2.24 + x + 2.24 + x2 = 0 + 2.24

Reorder the terms:
-2.24 + 2.24 + x + x2 = 0 + 2.24

Combine like terms: -2.24 + 2.24 = 0.00
0.00 + x + x2 = 0 + 2.24
x + x2 = 0 + 2.24

Combine like terms: 0 + 2.24 = 2.24
x + x2 = 2.24

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 2.24 + 0.25

Reorder the terms:
0.25 + x + x2 = 2.24 + 0.25

Combine like terms: 2.24 + 0.25 = 2.49
0.25 + x + x2 = 2.49

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.49

Calculate the square root of the right side: 1.577973384

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.577973384 and -1.577973384.


Subproblem 1
x + 0.5 = 1.577973384

Simplifying
x + 0.5 = 1.577973384

Reorder the terms:
0.5 + x = 1.577973384

Solving
0.5 + x = 1.577973384

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.577973384 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.577973384 + -0.5
x = 1.577973384 + -0.5

Combine like terms: 1.577973384 + -0.5 = 1.077973384
x = 1.077973384

Simplifying
x = 1.077973384


Subproblem 2
x + 0.5 = -1.577973384

Simplifying
x + 0.5 = -1.577973384

Reorder the terms:
0.5 + x = -1.577973384

Solving
0.5 + x = -1.577973384

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.577973384 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.577973384 + -0.5
x = -1.577973384 + -0.5

Combine like terms: -1.577973384 + -0.5 = -2.077973384
x = -2.077973384

Simplifying
x = -2.077973384


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.077973384, -2.077973384}

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