5x(x-3)-2=23

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Solution for 5x(x-3)-2=23 equation: 


Simplifying
5x(x + -3) + -2 = 23

Reorder the terms:
5x(-3 + x) + -2 = 23
(-3 * 5x + x * 5x) + -2 = 23
(-15x + 5x2) + -2 = 23

Reorder the terms:
-2 + -15x + 5x2 = 23

Solving
-2 + -15x + 5x2 = 23

Solving for variable 'x'.

Reorder the terms:
-2 + -23 + -15x + 5x2 = 23 + -23

Combine like terms: -2 + -23 = -25
-25 + -15x + 5x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-25 + -15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -3x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + -3x + x2 = 0

Solving
-5 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x + x2 = 0 + 5
-3x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3x + x2 = 5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3x + x2 = 7.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
x + -1.5 = 2.692582404

Simplifying
x + -1.5 = 2.692582404

Reorder the terms:
-1.5 + x = 2.692582404

Solving
-1.5 + x = 2.692582404

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.692582404 + 1.5
x = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
x = 4.192582404

Simplifying
x = 4.192582404


Subproblem 2
x + -1.5 = -2.692582404

Simplifying
x + -1.5 = -2.692582404

Reorder the terms:
-1.5 + x = -2.692582404

Solving
-1.5 + x = -2.692582404

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.692582404 + 1.5
x = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
x = -1.192582404

Simplifying
x = -1.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.192582404, -1.192582404}
Solution
x = {4.192582404, -1.192582404}

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