x^2+x=4.95

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Solution for x^2+x=4.95 equation: 


Simplifying
x2 + x = 4.95

Reorder the terms:
x + x2 = 4.95

Solving
x + x2 = 4.95

Solving for variable 'x'.

Reorder the terms:
-4.95 + x + x2 = 4.95 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
-4.95 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '4.95' to each side of the equation.
-4.95 + x + 4.95 + x2 = 0.00 + 4.95

Reorder the terms:
-4.95 + 4.95 + x + x2 = 0.00 + 4.95

Combine like terms: -4.95 + 4.95 = 0.00
0.00 + x + x2 = 0.00 + 4.95
x + x2 = 0.00 + 4.95

Combine like terms: 0.00 + 4.95 = 4.95
x + x2 = 4.95

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 = 4.95 + 0.25

Reorder the terms:
0.25 + x + x2 = 4.95 + 0.25

Combine like terms: 4.95 + 0.25 = 5.2
0.25 + x + x2 = 5.2

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.2

Calculate the square root of the right side: 2.28035085

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.28035085 and -2.28035085.


Subproblem 1
x + 0.5 = 2.28035085

Simplifying
x + 0.5 = 2.28035085

Reorder the terms:
0.5 + x = 2.28035085

Solving
0.5 + x = 2.28035085

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 = 2.28035085 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.28035085 + -0.5
x = 2.28035085 + -0.5

Combine like terms: 2.28035085 + -0.5 = 1.78035085
x = 1.78035085

Simplifying
x = 1.78035085


Subproblem 2
x + 0.5 = -2.28035085

Simplifying
x + 0.5 = -2.28035085

Reorder the terms:
0.5 + x = -2.28035085

Solving
0.5 + x = -2.28035085

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 = -2.28035085 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.28035085 + -0.5
x = -2.28035085 + -0.5

Combine like terms: -2.28035085 + -0.5 = -2.78035085
x = -2.78035085

Simplifying
x = -2.78035085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.78035085, -2.78035085}

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