x(x+5)=145

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Solution for x(x+5)=145 equation: 


Simplifying
x(x + 5) = 145

Reorder the terms:
x(5 + x) = 145
(5 * x + x * x) = 145
(5x + x2) = 145

Solving
5x + x2 = 145

Solving for variable 'x'.

Reorder the terms:
-145 + 5x + x2 = 145 + -145

Combine like terms: 145 + -145 = 0
-145 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '145' to each side of the equation.
-145 + 5x + 145 + x2 = 0 + 145

Reorder the terms:
-145 + 145 + 5x + x2 = 0 + 145

Combine like terms: -145 + 145 = 0
0 + 5x + x2 = 0 + 145
5x + x2 = 0 + 145

Combine like terms: 0 + 145 = 145
5x + x2 = 145

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 = 145 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 145 + 6.25

Combine like terms: 145 + 6.25 = 151.25
6.25 + 5x + x2 = 151.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 151.25

Calculate the square root of the right side: 12.298373876

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.298373876 and -12.298373876.


Subproblem 1
x + 2.5 = 12.298373876

Simplifying
x + 2.5 = 12.298373876

Reorder the terms:
2.5 + x = 12.298373876

Solving
2.5 + x = 12.298373876

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 = 12.298373876 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 12.298373876 + -2.5
x = 12.298373876 + -2.5

Combine like terms: 12.298373876 + -2.5 = 9.798373876
x = 9.798373876

Simplifying
x = 9.798373876


Subproblem 2
x + 2.5 = -12.298373876

Simplifying
x + 2.5 = -12.298373876

Reorder the terms:
2.5 + x = -12.298373876

Solving
2.5 + x = -12.298373876

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 = -12.298373876 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -12.298373876 + -2.5
x = -12.298373876 + -2.5

Combine like terms: -12.298373876 + -2.5 = -14.798373876
x = -14.798373876

Simplifying
x = -14.798373876


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.798373876, -14.798373876}

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