4.8=x^2+x

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Solution for 4.8=x^2+x equation: 


Simplifying
4.8 = x2 + x

Reorder the terms:
4.8 = x + x2

Solving
4.8 = x + x2

Solving for variable 'x'.

Reorder the terms:
4.8 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
4.8 + -1x + -1x2 = 0 + x2 + -1x2
4.8 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4.8 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4.8 + x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + x + x2 = 0 + 4.8
x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
x + x2 = 4.8

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.
 + 0.25 + x2 = 4.8 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 4.8 + 0.25

Combine like terms: 4.8 + 0.25 = 5.05
1.25 + x2 = 5.05

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.05

Calculate the square root of the right side: 2.247220505

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.247220505 and -2.247220505.


Subproblem 1
x + 0.5 = 2.247220505

Simplifying
x + 0.5 = 2.247220505

Reorder the terms:
0.5 + x = 2.247220505

Solving
0.5 + x = 2.247220505

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 = 2.247220505 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.247220505 + -0.5
x = 2.247220505 + -0.5

Combine like terms: 2.247220505 + -0.5 = 1.747220505
x = 1.747220505

Simplifying
x = 1.747220505


Subproblem 2
x + 0.5 = -2.247220505

Simplifying
x + 0.5 = -2.247220505

Reorder the terms:
0.5 + x = -2.247220505

Solving
0.5 + x = -2.247220505

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 = -2.247220505 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.247220505 + -0.5
x = -2.247220505 + -0.5

Combine like terms: -2.247220505 + -0.5 = -2.747220505
x = -2.747220505

Simplifying
x = -2.747220505


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.747220505, -2.747220505}

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