50=(x+10)x

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Solution for 50=(x+10)x equation:


Simplifying
50 = (x + 10) * x

Reorder the terms:
50 = (10 + x) * x

Reorder the terms for easier multiplication:
50 = x(10 + x)
50 = (10 * x + x * x)
50 = (10x + x2)

Solving
50 = 10x + x2

Solving for variable 'x'.

Reorder the terms:
50 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
50 + -10x + -1x2 = 0 + x2 + -1x2
50 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
50 + -10x + -1x2 = 0

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

Divide each side by '-1'.
-50 + 10x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 10x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 10x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 10x + x2 = 0 + 50
10x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
10x + x2 = 50

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 = 50 + 25

Reorder the terms:
25 + 10x + x2 = 50 + 25

Combine like terms: 50 + 25 = 75
25 + 10x + x2 = 75

Factor a perfect square on the left side:
(x + 5)(x + 5) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 5) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + 5 = 8.660254038

Simplifying
x + 5 = 8.660254038

Reorder the terms:
5 + x = 8.660254038

Solving
5 + x = 8.660254038

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 = 8.660254038 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.660254038 + -5
x = 8.660254038 + -5

Combine like terms: 8.660254038 + -5 = 3.660254038
x = 3.660254038

Simplifying
x = 3.660254038


Subproblem 2
x + 5 = -8.660254038

Simplifying
x + 5 = -8.660254038

Reorder the terms:
5 + x = -8.660254038

Solving
5 + x = -8.660254038

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 = -8.660254038 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.660254038 + -5
x = -8.660254038 + -5

Combine like terms: -8.660254038 + -5 = -13.660254038
x = -13.660254038

Simplifying
x = -13.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.660254038, -13.660254038}

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