x^2-14x+49=38

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Solution for x^2-14x+49=38 equation: 


Simplifying
x2 + -14x + 49 = 38

Reorder the terms:
49 + -14x + x2 = 38

Solving
49 + -14x + x2 = 38

Solving for variable 'x'.

Reorder the terms:
49 + -38 + -14x + x2 = 38 + -38

Combine like terms: 49 + -38 = 11
11 + -14x + x2 = 38 + -38

Combine like terms: 38 + -38 = 0
11 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -14x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -14x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -14x + x2 = 0 + -11
-14x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-14x + x2 = -11

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -11 + 49

Reorder the terms:
49 + -14x + x2 = -11 + 49

Combine like terms: -11 + 49 = 38
49 + -14x + x2 = 38

Factor a perfect square on the left side:
(x + -7)(x + -7) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + -7) equal to 6.164414003 and -6.164414003.


Subproblem 1
x + -7 = 6.164414003

Simplifying
x + -7 = 6.164414003

Reorder the terms:
-7 + x = 6.164414003

Solving
-7 + x = 6.164414003

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.164414003 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.164414003 + 7
x = 6.164414003 + 7

Combine like terms: 6.164414003 + 7 = 13.164414003
x = 13.164414003

Simplifying
x = 13.164414003


Subproblem 2
x + -7 = -6.164414003

Simplifying
x + -7 = -6.164414003

Reorder the terms:
-7 + x = -6.164414003

Solving
-7 + x = -6.164414003

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.164414003 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.164414003 + 7
x = -6.164414003 + 7

Combine like terms: -6.164414003 + 7 = 0.835585997
x = 0.835585997

Simplifying
x = 0.835585997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.164414003, 0.835585997}

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