5x(x-13)=140

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Solution for 5x(x-13)=140 equation: 


Simplifying
5x(x + -13) = 140

Reorder the terms:
5x(-13 + x) = 140
(-13 * 5x + x * 5x) = 140
(-65x + 5x2) = 140

Solving
-65x + 5x2 = 140

Solving for variable 'x'.

Reorder the terms:
-140 + -65x + 5x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + -65x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + -13x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-28 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -13x + x2 = 0

Solving
-28 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -13x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -13x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -13x + x2 = 0 + 28
-13x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-13x + x2 = 28

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 28 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 28 + 42.25

Combine like terms: 28 + 42.25 = 70.25
42.25 + -13x + x2 = 70.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + -6.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x + -6.5 = 8.381527307

Simplifying
x + -6.5 = 8.381527307

Reorder the terms:
-6.5 + x = 8.381527307

Solving
-6.5 + x = 8.381527307

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 8.381527307 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 8.381527307 + 6.5
x = 8.381527307 + 6.5

Combine like terms: 8.381527307 + 6.5 = 14.881527307
x = 14.881527307

Simplifying
x = 14.881527307


Subproblem 2
x + -6.5 = -8.381527307

Simplifying
x + -6.5 = -8.381527307

Reorder the terms:
-6.5 + x = -8.381527307

Solving
-6.5 + x = -8.381527307

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -8.381527307 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -8.381527307 + 6.5
x = -8.381527307 + 6.5

Combine like terms: -8.381527307 + 6.5 = -1.881527307
x = -1.881527307

Simplifying
x = -1.881527307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.881527307, -1.881527307}
Solution
x = {14.881527307, -1.881527307}

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