x(x+5)=88

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Solution for x(x+5)=88 equation: 


Simplifying
x(x + 5) = 88

Reorder the terms:
x(5 + x) = 88
(5 * x + x * x) = 88
(5x + x2) = 88

Solving
5x + x2 = 88

Solving for variable 'x'.

Reorder the terms:
-88 + 5x + x2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + 5x + 88 + x2 = 0 + 88

Reorder the terms:
-88 + 88 + 5x + x2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + 5x + x2 = 0 + 88
5x + x2 = 0 + 88

Combine like terms: 0 + 88 = 88
5x + x2 = 88

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 = 88 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 88 + 6.25

Combine like terms: 88 + 6.25 = 94.25
6.25 + 5x + x2 = 94.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 94.25

Calculate the square root of the right side: 9.708243919

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.708243919 and -9.708243919.


Subproblem 1
x + 2.5 = 9.708243919

Simplifying
x + 2.5 = 9.708243919

Reorder the terms:
2.5 + x = 9.708243919

Solving
2.5 + x = 9.708243919

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 = 9.708243919 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.708243919 + -2.5
x = 9.708243919 + -2.5

Combine like terms: 9.708243919 + -2.5 = 7.208243919
x = 7.208243919

Simplifying
x = 7.208243919


Subproblem 2
x + 2.5 = -9.708243919

Simplifying
x + 2.5 = -9.708243919

Reorder the terms:
2.5 + x = -9.708243919

Solving
2.5 + x = -9.708243919

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 = -9.708243919 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.708243919 + -2.5
x = -9.708243919 + -2.5

Combine like terms: -9.708243919 + -2.5 = -12.208243919
x = -12.208243919

Simplifying
x = -12.208243919


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.208243919, -12.208243919}

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