x^2-10x=49

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Solution for x^2-10x=49 equation: 


Simplifying
x2 + -10x = 49

Reorder the terms:
-10x + x2 = 49

Solving
-10x + x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + -10x + x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -10x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + -10x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -10x + x2 = 0 + 49
-10x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
-10x + x2 = 49

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 = 49 + 25

Reorder the terms:
25 + -10x + x2 = 49 + 25

Combine like terms: 49 + 25 = 74
25 + -10x + x2 = 74

Factor a perfect square on the left side:
(x + -5)(x + -5) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + -5) equal to 8.602325267 and -8.602325267.


Subproblem 1
x + -5 = 8.602325267

Simplifying
x + -5 = 8.602325267

Reorder the terms:
-5 + x = 8.602325267

Solving
-5 + x = 8.602325267

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 = 8.602325267 + 5

Combine like terms: -5 + 5 = 0
0 + x = 8.602325267 + 5
x = 8.602325267 + 5

Combine like terms: 8.602325267 + 5 = 13.602325267
x = 13.602325267

Simplifying
x = 13.602325267


Subproblem 2
x + -5 = -8.602325267

Simplifying
x + -5 = -8.602325267

Reorder the terms:
-5 + x = -8.602325267

Solving
-5 + x = -8.602325267

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 = -8.602325267 + 5

Combine like terms: -5 + 5 = 0
0 + x = -8.602325267 + 5
x = -8.602325267 + 5

Combine like terms: -8.602325267 + 5 = -3.602325267
x = -3.602325267

Simplifying
x = -3.602325267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.602325267, -3.602325267}

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