(30+x)x=176

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Solution for (30+x)x=176 equation: 


Simplifying
(30 + x) * x = 176

Reorder the terms for easier multiplication:
x(30 + x) = 176
(30 * x + x * x) = 176
(30x + x2) = 176

Solving
30x + x2 = 176

Solving for variable 'x'.

Reorder the terms:
-176 + 30x + x2 = 176 + -176

Combine like terms: 176 + -176 = 0
-176 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '176' to each side of the equation.
-176 + 30x + 176 + x2 = 0 + 176

Reorder the terms:
-176 + 176 + 30x + x2 = 0 + 176

Combine like terms: -176 + 176 = 0
0 + 30x + x2 = 0 + 176
30x + x2 = 0 + 176

Combine like terms: 0 + 176 = 176
30x + x2 = 176

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 176 + 225

Reorder the terms:
225 + 30x + x2 = 176 + 225

Combine like terms: 176 + 225 = 401
225 + 30x + x2 = 401

Factor a perfect square on the left side:
(x + 15)(x + 15) = 401

Calculate the square root of the right side: 20.024984395

Break this problem into two subproblems by setting 
(x + 15) equal to 20.024984395 and -20.024984395.


Subproblem 1
x + 15 = 20.024984395

Simplifying
x + 15 = 20.024984395

Reorder the terms:
15 + x = 20.024984395

Solving
15 + x = 20.024984395

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 20.024984395 + -15

Combine like terms: 15 + -15 = 0
0 + x = 20.024984395 + -15
x = 20.024984395 + -15

Combine like terms: 20.024984395 + -15 = 5.024984395
x = 5.024984395

Simplifying
x = 5.024984395


Subproblem 2
x + 15 = -20.024984395

Simplifying
x + 15 = -20.024984395

Reorder the terms:
15 + x = -20.024984395

Solving
15 + x = -20.024984395

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -20.024984395 + -15

Combine like terms: 15 + -15 = 0
0 + x = -20.024984395 + -15
x = -20.024984395 + -15

Combine like terms: -20.024984395 + -15 = -35.024984395
x = -35.024984395

Simplifying
x = -35.024984395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.024984395, -35.024984395}

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