x(x+5)=74

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Solution for x(x+5)=74 equation: 


Simplifying
x(x + 5) = 74

Reorder the terms:
x(5 + x) = 74
(5 * x + x * x) = 74
(5x + x2) = 74

Solving
5x + x2 = 74

Solving for variable 'x'.

Reorder the terms:
-74 + 5x + x2 = 74 + -74

Combine like terms: 74 + -74 = 0
-74 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + 5x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + 5x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 5x + x2 = 0 + 74
5x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
5x + x2 = 74

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 = 74 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 74 + 6.25

Combine like terms: 74 + 6.25 = 80.25
6.25 + 5x + x2 = 80.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.958236434 and -8.958236434.


Subproblem 1
x + 2.5 = 8.958236434

Simplifying
x + 2.5 = 8.958236434

Reorder the terms:
2.5 + x = 8.958236434

Solving
2.5 + x = 8.958236434

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 = 8.958236434 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.958236434 + -2.5
x = 8.958236434 + -2.5

Combine like terms: 8.958236434 + -2.5 = 6.458236434
x = 6.458236434

Simplifying
x = 6.458236434


Subproblem 2
x + 2.5 = -8.958236434

Simplifying
x + 2.5 = -8.958236434

Reorder the terms:
2.5 + x = -8.958236434

Solving
2.5 + x = -8.958236434

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 = -8.958236434 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.958236434 + -2.5
x = -8.958236434 + -2.5

Combine like terms: -8.958236434 + -2.5 = -11.458236434
x = -11.458236434

Simplifying
x = -11.458236434


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.458236434, -11.458236434}

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