40=2x^2-6x

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Solution for 40=2x^2-6x equation: 


Simplifying
40 = 2x2 + -6x

Reorder the terms:
40 = -6x + 2x2

Solving
40 = -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
40 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
40 + 6x + -2x2 = 0 + 2x2 + -2x2
40 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + 6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 3x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
20 + 3x + -1x2 = 0

Solving
20 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-20 + -3x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -3x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -3x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3x + x2 = 0 + 20
-3x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-3x + x2 = 20

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 = 20 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + -3x + x2 = 22.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + -1.5 = 4.716990566

Simplifying
x + -1.5 = 4.716990566

Reorder the terms:
-1.5 + x = 4.716990566

Solving
-1.5 + x = 4.716990566

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 = 4.716990566 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.716990566 + 1.5
x = 4.716990566 + 1.5

Combine like terms: 4.716990566 + 1.5 = 6.216990566
x = 6.216990566

Simplifying
x = 6.216990566


Subproblem 2
x + -1.5 = -4.716990566

Simplifying
x + -1.5 = -4.716990566

Reorder the terms:
-1.5 + x = -4.716990566

Solving
-1.5 + x = -4.716990566

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 = -4.716990566 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.716990566 + 1.5
x = -4.716990566 + 1.5

Combine like terms: -4.716990566 + 1.5 = -3.216990566
x = -3.216990566

Simplifying
x = -3.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.216990566, -3.216990566}
Solution
x = {6.216990566, -3.216990566}

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