3x(x-5)-5-2=3

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Solution for 3x(x-5)-5-2=3 equation: 


Simplifying
3x(x + -5) + -5 + -2 = 3

Reorder the terms:
3x(-5 + x) + -5 + -2 = 3
(-5 * 3x + x * 3x) + -5 + -2 = 3
(-15x + 3x2) + -5 + -2 = 3

Reorder the terms:
-5 + -2 + -15x + 3x2 = 3

Combine like terms: -5 + -2 = -7
-7 + -15x + 3x2 = 3

Solving
-7 + -15x + 3x2 = 3

Solving for variable 'x'.

Reorder the terms:
-7 + -3 + -15x + 3x2 = 3 + -3

Combine like terms: -7 + -3 = -10
-10 + -15x + 3x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-10 + -15x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -5x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -5x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + 3.333333333
-5x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-5x + x2 = 3.333333333

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 = 3.333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3.333333333 + 6.25

Combine like terms: 3.333333333 + 6.25 = 9.583333333
6.25 + -5x + x2 = 9.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.583333333

Calculate the square root of the right side: 3.095695937

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.095695937 and -3.095695937.


Subproblem 1
x + -2.5 = 3.095695937

Simplifying
x + -2.5 = 3.095695937

Reorder the terms:
-2.5 + x = 3.095695937

Solving
-2.5 + x = 3.095695937

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 = 3.095695937 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.095695937 + 2.5
x = 3.095695937 + 2.5

Combine like terms: 3.095695937 + 2.5 = 5.595695937
x = 5.595695937

Simplifying
x = 5.595695937


Subproblem 2
x + -2.5 = -3.095695937

Simplifying
x + -2.5 = -3.095695937

Reorder the terms:
-2.5 + x = -3.095695937

Solving
-2.5 + x = -3.095695937

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 = -3.095695937 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.095695937 + 2.5
x = -3.095695937 + 2.5

Combine like terms: -3.095695937 + 2.5 = -0.595695937
x = -0.595695937

Simplifying
x = -0.595695937


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.595695937, -0.595695937}

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