2(x^2-6x+9)+5x=7x

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Solution for 2(x^2-6x+9)+5x=7x equation: 


Simplifying
2(x2 + -6x + 9) + 5x = 7x

Reorder the terms:
2(9 + -6x + x2) + 5x = 7x
(9 * 2 + -6x * 2 + x2 * 2) + 5x = 7x
(18 + -12x + 2x2) + 5x = 7x

Reorder the terms:
18 + -12x + 5x + 2x2 = 7x

Combine like terms: -12x + 5x = -7x
18 + -7x + 2x2 = 7x

Solving
18 + -7x + 2x2 = 7x

Solving for variable 'x'.

Reorder the terms:
18 + -7x + -7x + 2x2 = 7x + -7x

Combine like terms: -7x + -7x = -14x
18 + -14x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
18 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
9 + -7x + x2 = 0

Solving
9 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -7x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -7x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x + x2 = 0 + -9
-7x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-7x + x2 = -9

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -9 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -9 + 12.25

Combine like terms: -9 + 12.25 = 3.25
12.25 + -7x + x2 = 3.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -3.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + -3.5 = 1.802775638

Simplifying
x + -3.5 = 1.802775638

Reorder the terms:
-3.5 + x = 1.802775638

Solving
-3.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 1.802775638 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 1.802775638 + 3.5
x = 1.802775638 + 3.5

Combine like terms: 1.802775638 + 3.5 = 5.302775638
x = 5.302775638

Simplifying
x = 5.302775638


Subproblem 2
x + -3.5 = -1.802775638

Simplifying
x + -3.5 = -1.802775638

Reorder the terms:
-3.5 + x = -1.802775638

Solving
-3.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -1.802775638 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -1.802775638 + 3.5
x = -1.802775638 + 3.5

Combine like terms: -1.802775638 + 3.5 = 1.697224362
x = 1.697224362

Simplifying
x = 1.697224362


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.302775638, 1.697224362}
Solution
x = {5.302775638, 1.697224362}

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