3x(2x-7)=3

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Solution for 3x(2x-7)=3 equation: 


Simplifying
3x(2x + -7) = 3

Reorder the terms:
3x(-7 + 2x) = 3
(-7 * 3x + 2x * 3x) = 3
(-21x + 6x2) = 3

Solving
-21x + 6x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -21x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -7x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -7x + 2x2 = 0

Solving
-1 + -7x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3.5x + x2 = 0 + 0.5
-3.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3.5x + x2 = 0.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 0.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 0.5 + 3.0625

Combine like terms: 0.5 + 3.0625 = 3.5625
3.0625 + -3.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.887458609 and -1.887458609.


Subproblem 1
x + -1.75 = 1.887458609

Simplifying
x + -1.75 = 1.887458609

Reorder the terms:
-1.75 + x = 1.887458609

Solving
-1.75 + x = 1.887458609

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.887458609 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.887458609 + 1.75
x = 1.887458609 + 1.75

Combine like terms: 1.887458609 + 1.75 = 3.637458609
x = 3.637458609

Simplifying
x = 3.637458609


Subproblem 2
x + -1.75 = -1.887458609

Simplifying
x + -1.75 = -1.887458609

Reorder the terms:
-1.75 + x = -1.887458609

Solving
-1.75 + x = -1.887458609

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.887458609 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.887458609 + 1.75
x = -1.887458609 + 1.75

Combine like terms: -1.887458609 + 1.75 = -0.137458609
x = -0.137458609

Simplifying
x = -0.137458609


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.637458609, -0.137458609}
Solution
x = {3.637458609, -0.137458609}

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