12x=2x^2-7x+3

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Solution for 12x=2x^2-7x+3 equation: 


Simplifying
12x = 2x2 + -7x + 3

Reorder the terms:
12x = 3 + -7x + 2x2

Solving
12x = 3 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + 12x + 7x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Combine like terms: 12x + 7x = 19x
-3 + 19x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Reorder the terms:
-3 + 19x + -2x2 = 3 + -3 + -7x + 7x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-3 + 19x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
-3 + 19x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-3 + 19x + -2x2 = 0 + 2x2 + -2x2
-3 + 19x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 19x + -2x2 = 0

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

Divide each side by '-2'.
1.5 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -9.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -9.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -9.5x + x2 = 0 + -1.5
-9.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-9.5x + x2 = -1.5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -1.5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -1.5 + 22.5625

Combine like terms: -1.5 + 22.5625 = 21.0625
22.5625 + -9.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.589389938 and -4.589389938.


Subproblem 1
x + -4.75 = 4.589389938

Simplifying
x + -4.75 = 4.589389938

Reorder the terms:
-4.75 + x = 4.589389938

Solving
-4.75 + x = 4.589389938

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 4.589389938 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 4.589389938 + 4.75
x = 4.589389938 + 4.75

Combine like terms: 4.589389938 + 4.75 = 9.339389938
x = 9.339389938

Simplifying
x = 9.339389938


Subproblem 2
x + -4.75 = -4.589389938

Simplifying
x + -4.75 = -4.589389938

Reorder the terms:
-4.75 + x = -4.589389938

Solving
-4.75 + x = -4.589389938

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -4.589389938 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -4.589389938 + 4.75
x = -4.589389938 + 4.75

Combine like terms: -4.589389938 + 4.75 = 0.160610062
x = 0.160610062

Simplifying
x = 0.160610062


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.339389938, 0.160610062}

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