x^2-18x+22=7x+4

Solution for x^2-18x+22=7x+4 equation:

Simplifying
x2 + -18x + 22 = 7x + 4

Reorder the terms:
22 + -18x + x2 = 7x + 4

Reorder the terms:
22 + -18x + x2 = 4 + 7x

Solving
22 + -18x + x2 = 4 + 7x

Solving for variable 'x'.

Reorder the terms:
22 + -4 + -18x + -7x + x2 = 4 + 7x + -4 + -7x

Combine like terms: 22 + -4 = 18
18 + -18x + -7x + x2 = 4 + 7x + -4 + -7x

Combine like terms: -18x + -7x = -25x
18 + -25x + x2 = 4 + 7x + -4 + -7x

Reorder the terms:
18 + -25x + x2 = 4 + -4 + 7x + -7x

Combine like terms: 4 + -4 = 0
18 + -25x + x2 = 0 + 7x + -7x
18 + -25x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
18 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -25x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -25x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -25x + x2 = 0 + -18
-25x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-25x + x2 = -18

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -18 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -18 + 156.25

Combine like terms: -18 + 156.25 = 138.25
156.25 + -25x + x2 = 138.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 138.25

Calculate the square root of the right side: 11.757976016

Break this problem into two subproblems by setting 
(x + -12.5) equal to 11.757976016 and -11.757976016.

Subproblem 1
x + -12.5 = 11.757976016

Simplifying
x + -12.5 = 11.757976016

Reorder the terms:
-12.5 + x = 11.757976016

Solving
-12.5 + x = 11.757976016

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 11.757976016 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 11.757976016 + 12.5
x = 11.757976016 + 12.5

Combine like terms: 11.757976016 + 12.5 = 24.257976016
x = 24.257976016

Simplifying
x = 24.257976016

Subproblem 2
x + -12.5 = -11.757976016

Simplifying
x + -12.5 = -11.757976016

Reorder the terms:
-12.5 + x = -11.757976016

Solving
-12.5 + x = -11.757976016

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -11.757976016 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -11.757976016 + 12.5
x = -11.757976016 + 12.5

Combine like terms: -11.757976016 + 12.5 = 0.742023984
x = 0.742023984

Simplifying
x = 0.742023984

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.257976016, 0.742023984}