(x+7)x=50

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Solution for (x+7)x=50 equation:


Simplifying
(x + 7) * x = 50

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

Reorder the terms for easier multiplication:
x(7 + x) = 50
(7 * x + x * x) = 50
(7x + x2) = 50

Solving
7x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + 7x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 7x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 7x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 7x + x2 = 0 + 50
7x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
7x + x2 = 50

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 50 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 50 + 12.25

Combine like terms: 50 + 12.25 = 62.25
12.25 + 7x + x2 = 62.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.889866919 and -7.889866919.


Subproblem 1
x + 3.5 = 7.889866919

Simplifying
x + 3.5 = 7.889866919

Reorder the terms:
3.5 + x = 7.889866919

Solving
3.5 + x = 7.889866919

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 7.889866919 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7.889866919 + -3.5
x = 7.889866919 + -3.5

Combine like terms: 7.889866919 + -3.5 = 4.389866919
x = 4.389866919

Simplifying
x = 4.389866919


Subproblem 2
x + 3.5 = -7.889866919

Simplifying
x + 3.5 = -7.889866919

Reorder the terms:
3.5 + x = -7.889866919

Solving
3.5 + x = -7.889866919

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -7.889866919 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7.889866919 + -3.5
x = -7.889866919 + -3.5

Combine like terms: -7.889866919 + -3.5 = -11.389866919
x = -11.389866919

Simplifying
x = -11.389866919


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.389866919, -11.389866919}

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