x^2-14x=49

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


Simplifying
x2 + -14x = 49

Reorder the terms:
-14x + x2 = 49

Solving
-14x + x2 = 49

Solving for variable 'x'.

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

Combine like terms: 49 + -49 = 0
-49 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -14x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + -14x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -14x + x2 = 0 + 49
-14x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
-14x + x2 = 49

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 = 49 + 49

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

Combine like terms: 49 + 49 = 98
49 + -14x + x2 = 98

Factor a perfect square on the left side:
(x + -7)(x + -7) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + -7) equal to 9.899494937 and -9.899494937.


Subproblem 1
x + -7 = 9.899494937

Simplifying
x + -7 = 9.899494937

Reorder the terms:
-7 + x = 9.899494937

Solving
-7 + x = 9.899494937

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 = 9.899494937 + 7

Combine like terms: -7 + 7 = 0
0 + x = 9.899494937 + 7
x = 9.899494937 + 7

Combine like terms: 9.899494937 + 7 = 16.899494937
x = 16.899494937

Simplifying
x = 16.899494937


Subproblem 2
x + -7 = -9.899494937

Simplifying
x + -7 = -9.899494937

Reorder the terms:
-7 + x = -9.899494937

Solving
-7 + x = -9.899494937

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 = -9.899494937 + 7

Combine like terms: -7 + 7 = 0
0 + x = -9.899494937 + 7
x = -9.899494937 + 7

Combine like terms: -9.899494937 + 7 = -2.899494937
x = -2.899494937

Simplifying
x = -2.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.899494937, -2.899494937}

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