2x(x-5)=3

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


Simplifying
2x(x + -5) = 3

Reorder the terms:
2x(-5 + x) = 3
(-5 * 2x + x * 2x) = 3
(-10x + 2x2) = 3

Solving
-10x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -10x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -10x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + -5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -5x + x2 = 0 + 1.5
-5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-5x + x2 = 1.5

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 = 1.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1.5 + 6.25

Combine like terms: 1.5 + 6.25 = 7.75
6.25 + -5x + x2 = 7.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.783882181 and -2.783882181.


Subproblem 1
x + -2.5 = 2.783882181

Simplifying
x + -2.5 = 2.783882181

Reorder the terms:
-2.5 + x = 2.783882181

Solving
-2.5 + x = 2.783882181

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 = 2.783882181 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.783882181 + 2.5
x = 2.783882181 + 2.5

Combine like terms: 2.783882181 + 2.5 = 5.283882181
x = 5.283882181

Simplifying
x = 5.283882181


Subproblem 2
x + -2.5 = -2.783882181

Simplifying
x + -2.5 = -2.783882181

Reorder the terms:
-2.5 + x = -2.783882181

Solving
-2.5 + x = -2.783882181

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 = -2.783882181 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.783882181 + 2.5
x = -2.783882181 + 2.5

Combine like terms: -2.783882181 + 2.5 = -0.283882181
x = -0.283882181

Simplifying
x = -0.283882181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.283882181, -0.283882181}

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