((x+11)+24)x=1752

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Solution for ((x+11)+24)x=1752 equation: 


Simplifying
((x + 11) + 24) * x = 1752

Reorder the terms:
((11 + x) + 24) * x = 1752

Remove parenthesis around (11 + x)
(11 + x + 24) * x = 1752

Reorder the terms:
(11 + 24 + x) * x = 1752

Combine like terms: 11 + 24 = 35
(35 + x) * x = 1752

Reorder the terms for easier multiplication:
x(35 + x) = 1752
(35 * x + x * x) = 1752
(35x + x2) = 1752

Solving
35x + x2 = 1752

Solving for variable 'x'.

Reorder the terms:
-1752 + 35x + x2 = 1752 + -1752

Combine like terms: 1752 + -1752 = 0
-1752 + 35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1752' to each side of the equation.
-1752 + 35x + 1752 + x2 = 0 + 1752

Reorder the terms:
-1752 + 1752 + 35x + x2 = 0 + 1752

Combine like terms: -1752 + 1752 = 0
0 + 35x + x2 = 0 + 1752
35x + x2 = 0 + 1752

Combine like terms: 0 + 1752 = 1752
35x + x2 = 1752

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 1752 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 1752 + 306.25

Combine like terms: 1752 + 306.25 = 2058.25
306.25 + 35x + x2 = 2058.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 2058.25

Calculate the square root of the right side: 45.367940222

Break this problem into two subproblems by setting 
(x + 17.5) equal to 45.367940222 and -45.367940222.


Subproblem 1
x + 17.5 = 45.367940222

Simplifying
x + 17.5 = 45.367940222

Reorder the terms:
17.5 + x = 45.367940222

Solving
17.5 + x = 45.367940222

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 45.367940222 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 45.367940222 + -17.5
x = 45.367940222 + -17.5

Combine like terms: 45.367940222 + -17.5 = 27.867940222
x = 27.867940222

Simplifying
x = 27.867940222


Subproblem 2
x + 17.5 = -45.367940222

Simplifying
x + 17.5 = -45.367940222

Reorder the terms:
17.5 + x = -45.367940222

Solving
17.5 + x = -45.367940222

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -45.367940222 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -45.367940222 + -17.5
x = -45.367940222 + -17.5

Combine like terms: -45.367940222 + -17.5 = -62.867940222
x = -62.867940222

Simplifying
x = -62.867940222


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.867940222, -62.867940222}

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