x^2-10x=73

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Solution for x^2-10x=73 equation: 


Simplifying
x2 + -10x = 73

Reorder the terms:
-10x + x2 = 73

Solving
-10x + x2 = 73

Solving for variable 'x'.

Reorder the terms:
-73 + -10x + x2 = 73 + -73

Combine like terms: 73 + -73 = 0
-73 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + -10x + 73 + x2 = 0 + 73

Reorder the terms:
-73 + 73 + -10x + x2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + -10x + x2 = 0 + 73
-10x + x2 = 0 + 73

Combine like terms: 0 + 73 = 73
-10x + x2 = 73

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 73 + 25

Reorder the terms:
25 + -10x + x2 = 73 + 25

Combine like terms: 73 + 25 = 98
25 + -10x + x2 = 98

Factor a perfect square on the left side:
(x + -5)(x + -5) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + -5) equal to 9.899494937 and -9.899494937.


Subproblem 1
x + -5 = 9.899494937

Simplifying
x + -5 = 9.899494937

Reorder the terms:
-5 + x = 9.899494937

Solving
-5 + x = 9.899494937

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 9.899494937 + 5

Combine like terms: -5 + 5 = 0
0 + x = 9.899494937 + 5
x = 9.899494937 + 5

Combine like terms: 9.899494937 + 5 = 14.899494937
x = 14.899494937

Simplifying
x = 14.899494937


Subproblem 2
x + -5 = -9.899494937

Simplifying
x + -5 = -9.899494937

Reorder the terms:
-5 + x = -9.899494937

Solving
-5 + x = -9.899494937

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -9.899494937 + 5

Combine like terms: -5 + 5 = 0
0 + x = -9.899494937 + 5
x = -9.899494937 + 5

Combine like terms: -9.899494937 + 5 = -4.899494937
x = -4.899494937

Simplifying
x = -4.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.899494937, -4.899494937}

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