x(175+x)=30625

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Solution for x(175+x)=30625 equation: 


Simplifying
x(175 + x) = 30625
(175 * x + x * x) = 30625
(175x + x2) = 30625

Solving
175x + x2 = 30625

Solving for variable 'x'.

Reorder the terms:
-30625 + 175x + x2 = 30625 + -30625

Combine like terms: 30625 + -30625 = 0
-30625 + 175x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30625' to each side of the equation.
-30625 + 175x + 30625 + x2 = 0 + 30625

Reorder the terms:
-30625 + 30625 + 175x + x2 = 0 + 30625

Combine like terms: -30625 + 30625 = 0
0 + 175x + x2 = 0 + 30625
175x + x2 = 0 + 30625

Combine like terms: 0 + 30625 = 30625
175x + x2 = 30625

The x term is 175x.  Take half its coefficient (87.5).
Square it (7656.25) and add it to both sides.

Add '7656.25' to each side of the equation.
175x + 7656.25 + x2 = 30625 + 7656.25

Reorder the terms:
7656.25 + 175x + x2 = 30625 + 7656.25

Combine like terms: 30625 + 7656.25 = 38281.25
7656.25 + 175x + x2 = 38281.25

Factor a perfect square on the left side:
(x + 87.5)(x + 87.5) = 38281.25

Calculate the square root of the right side: 195.655948031

Break this problem into two subproblems by setting 
(x + 87.5) equal to 195.655948031 and -195.655948031.


Subproblem 1
x + 87.5 = 195.655948031

Simplifying
x + 87.5 = 195.655948031

Reorder the terms:
87.5 + x = 195.655948031

Solving
87.5 + x = 195.655948031

Solving for variable 'x'.

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

Add '-87.5' to each side of the equation.
87.5 + -87.5 + x = 195.655948031 + -87.5

Combine like terms: 87.5 + -87.5 = 0.0
0.0 + x = 195.655948031 + -87.5
x = 195.655948031 + -87.5

Combine like terms: 195.655948031 + -87.5 = 108.155948031
x = 108.155948031

Simplifying
x = 108.155948031


Subproblem 2
x + 87.5 = -195.655948031

Simplifying
x + 87.5 = -195.655948031

Reorder the terms:
87.5 + x = -195.655948031

Solving
87.5 + x = -195.655948031

Solving for variable 'x'.

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

Add '-87.5' to each side of the equation.
87.5 + -87.5 + x = -195.655948031 + -87.5

Combine like terms: 87.5 + -87.5 = 0.0
0.0 + x = -195.655948031 + -87.5
x = -195.655948031 + -87.5

Combine like terms: -195.655948031 + -87.5 = -283.155948031
x = -283.155948031

Simplifying
x = -283.155948031


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {108.155948031, -283.155948031}

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