x^2-49=2x^2-23x+67

Solution for x^2-49=2x^2-23x+67 equation:

Simplifying
x2 + -49 = 2x2 + -23x + 67

Reorder the terms:
-49 + x2 = 2x2 + -23x + 67

Reorder the terms:
-49 + x2 = 67 + -23x + 2x2

Solving
-49 + x2 = 67 + -23x + 2x2

Solving for variable 'x'.

Reorder the terms:
-49 + -67 + 23x + x2 + -2x2 = 67 + -23x + 2x2 + -67 + 23x + -2x2

Combine like terms: -49 + -67 = -116
-116 + 23x + x2 + -2x2 = 67 + -23x + 2x2 + -67 + 23x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-116 + 23x + -1x2 = 67 + -23x + 2x2 + -67 + 23x + -2x2

Reorder the terms:
-116 + 23x + -1x2 = 67 + -67 + -23x + 23x + 2x2 + -2x2

Combine like terms: 67 + -67 = 0
-116 + 23x + -1x2 = 0 + -23x + 23x + 2x2 + -2x2
-116 + 23x + -1x2 = -23x + 23x + 2x2 + -2x2

Combine like terms: -23x + 23x = 0
-116 + 23x + -1x2 = 0 + 2x2 + -2x2
-116 + 23x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-116 + 23x + -1x2 = 0

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

Divide each side by '-1'.
116 + -23x + x2 = 0

Move the constant term to the right:

Add '-116' to each side of the equation.
116 + -23x + -116 + x2 = 0 + -116

Reorder the terms:
116 + -116 + -23x + x2 = 0 + -116

Combine like terms: 116 + -116 = 0
0 + -23x + x2 = 0 + -116
-23x + x2 = 0 + -116

Combine like terms: 0 + -116 = -116
-23x + x2 = -116

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -116 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -116 + 132.25

Combine like terms: -116 + 132.25 = 16.25
132.25 + -23x + x2 = 16.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + -11.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
x + -11.5 = 4.031128874

Simplifying
x + -11.5 = 4.031128874

Reorder the terms:
-11.5 + x = 4.031128874

Solving
-11.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 4.031128874 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 4.031128874 + 11.5
x = 4.031128874 + 11.5

Combine like terms: 4.031128874 + 11.5 = 15.531128874
x = 15.531128874

Simplifying
x = 15.531128874

Subproblem 2
x + -11.5 = -4.031128874

Simplifying
x + -11.5 = -4.031128874

Reorder the terms:
-11.5 + x = -4.031128874

Solving
-11.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -4.031128874 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -4.031128874 + 11.5
x = -4.031128874 + 11.5

Combine like terms: -4.031128874 + 11.5 = 7.468871126
x = 7.468871126

Simplifying
x = 7.468871126

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.531128874, 7.468871126}