X(X-5)=134

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Solution for X(X-5)=134 equation: 


Simplifying
X(X + -5) = 134

Reorder the terms:
X(-5 + X) = 134
(-5 * X + X * X) = 134
(-5X + X2) = 134

Solving
-5X + X2 = 134

Solving for variable 'X'.

Reorder the terms:
-134 + -5X + X2 = 134 + -134

Combine like terms: 134 + -134 = 0
-134 + -5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '134' to each side of the equation.
-134 + -5X + 134 + X2 = 0 + 134

Reorder the terms:
-134 + 134 + -5X + X2 = 0 + 134

Combine like terms: -134 + 134 = 0
0 + -5X + X2 = 0 + 134
-5X + X2 = 0 + 134

Combine like terms: 0 + 134 = 134
-5X + X2 = 134

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 = 134 + 6.25

Reorder the terms:
6.25 + -5X + X2 = 134 + 6.25

Combine like terms: 134 + 6.25 = 140.25
6.25 + -5X + X2 = 140.25

Factor a perfect square on the left side:
(X + -2.5)(X + -2.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(X + -2.5) equal to 11.842719282 and -11.842719282.


Subproblem 1
X + -2.5 = 11.842719282

Simplifying
X + -2.5 = 11.842719282

Reorder the terms:
-2.5 + X = 11.842719282

Solving
-2.5 + X = 11.842719282

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 = 11.842719282 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + X = 11.842719282 + 2.5
X = 11.842719282 + 2.5

Combine like terms: 11.842719282 + 2.5 = 14.342719282
X = 14.342719282

Simplifying
X = 14.342719282


Subproblem 2
X + -2.5 = -11.842719282

Simplifying
X + -2.5 = -11.842719282

Reorder the terms:
-2.5 + X = -11.842719282

Solving
-2.5 + X = -11.842719282

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 = -11.842719282 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + X = -11.842719282 + 2.5
X = -11.842719282 + 2.5

Combine like terms: -11.842719282 + 2.5 = -9.342719282
X = -9.342719282

Simplifying
X = -9.342719282


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {14.342719282, -9.342719282}

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