(4+x)x=175

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Solution for (4+x)x=175 equation: 


Simplifying
(4 + x) * x = 175

Reorder the terms for easier multiplication:
x(4 + x) = 175
(4 * x + x * x) = 175
(4x + x2) = 175

Solving
4x + x2 = 175

Solving for variable 'x'.

Reorder the terms:
-175 + 4x + x2 = 175 + -175

Combine like terms: 175 + -175 = 0
-175 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + 4x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + 4x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 4x + x2 = 0 + 175
4x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
4x + x2 = 175

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 175 + 4

Reorder the terms:
4 + 4x + x2 = 175 + 4

Combine like terms: 175 + 4 = 179
4 + 4x + x2 = 179

Factor a perfect square on the left side:
(x + 2)(x + 2) = 179

Calculate the square root of the right side: 13.37908816

Break this problem into two subproblems by setting 
(x + 2) equal to 13.37908816 and -13.37908816.


Subproblem 1
x + 2 = 13.37908816

Simplifying
x + 2 = 13.37908816

Reorder the terms:
2 + x = 13.37908816

Solving
2 + x = 13.37908816

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 13.37908816 + -2

Combine like terms: 2 + -2 = 0
0 + x = 13.37908816 + -2
x = 13.37908816 + -2

Combine like terms: 13.37908816 + -2 = 11.37908816
x = 11.37908816

Simplifying
x = 11.37908816


Subproblem 2
x + 2 = -13.37908816

Simplifying
x + 2 = -13.37908816

Reorder the terms:
2 + x = -13.37908816

Solving
2 + x = -13.37908816

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -13.37908816 + -2

Combine like terms: 2 + -2 = 0
0 + x = -13.37908816 + -2
x = -13.37908816 + -2

Combine like terms: -13.37908816 + -2 = -15.37908816
x = -15.37908816

Simplifying
x = -15.37908816


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.37908816, -15.37908816}

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