5x+x*x=2532

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Solution for 5x+x*x=2532 equation: 


Simplifying
5x + x * x = 2532

Multiply x * x
5x + x2 = 2532

Solving
5x + x2 = 2532

Solving for variable 'x'.

Reorder the terms:
-2532 + 5x + x2 = 2532 + -2532

Combine like terms: 2532 + -2532 = 0
-2532 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2532' to each side of the equation.
-2532 + 5x + 2532 + x2 = 0 + 2532

Reorder the terms:
-2532 + 2532 + 5x + x2 = 0 + 2532

Combine like terms: -2532 + 2532 = 0
0 + 5x + x2 = 0 + 2532
5x + x2 = 0 + 2532

Combine like terms: 0 + 2532 = 2532
5x + x2 = 2532

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2532 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2532 + 6.25

Combine like terms: 2532 + 6.25 = 2538.25
6.25 + 5x + x2 = 2538.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 2538.25

Calculate the square root of the right side: 50.381048024

Break this problem into two subproblems by setting 
(x + 2.5) equal to 50.381048024 and -50.381048024.


Subproblem 1
x + 2.5 = 50.381048024

Simplifying
x + 2.5 = 50.381048024

Reorder the terms:
2.5 + x = 50.381048024

Solving
2.5 + x = 50.381048024

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 50.381048024 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 50.381048024 + -2.5
x = 50.381048024 + -2.5

Combine like terms: 50.381048024 + -2.5 = 47.881048024
x = 47.881048024

Simplifying
x = 47.881048024


Subproblem 2
x + 2.5 = -50.381048024

Simplifying
x + 2.5 = -50.381048024

Reorder the terms:
2.5 + x = -50.381048024

Solving
2.5 + x = -50.381048024

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -50.381048024 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -50.381048024 + -2.5
x = -50.381048024 + -2.5

Combine like terms: -50.381048024 + -2.5 = -52.881048024
x = -52.881048024

Simplifying
x = -52.881048024


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.881048024, -52.881048024}

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