7=(x^2)+x+3

Solution for 7=(x^2)+x+3 equation:

Simplifying
7 = (x2) + x + 3
7 = x2 + x + 3

Reorder the terms:
7 = 3 + x + x2

Solving
7 = 3 + x + x2

Solving for variable 'x'.

Combine like terms: 7 + -3 = 4
4 + -1x + -1x2 = 3 + x + x2 + -3 + -1x + -1x2

Reorder the terms:
4 + -1x + -1x2 = 3 + -3 + x + -1x + x2 + -1x2

Combine like terms: 3 + -3 = 0
4 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
4 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
4 + -1x + -1x2 = 0 + x2 + -1x2
4 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-4 + x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x + x2 = 0 + 4
x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
x + x2 = 4

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 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
1.25 + x2 = 4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + 0.5 = 2.061552813

Simplifying
x + 0.5 = 2.061552813

Reorder the terms:
0.5 + x = 2.061552813

Solving
0.5 + x = 2.061552813

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 = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.061552813 + -0.5
x = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
x = 1.561552813

Simplifying
x = 1.561552813

Subproblem 2
x + 0.5 = -2.061552813

Simplifying
x + 0.5 = -2.061552813

Reorder the terms:
0.5 + x = -2.061552813

Solving
0.5 + x = -2.061552813

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 = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.061552813 + -0.5
x = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
x = -2.561552813

Simplifying
x = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.561552813, -2.561552813}