3x(x-2)=x-7

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


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

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

Reorder the terms:
-6x + 3x2 = -7 + x

Solving
-6x + 3x2 = -7 + x

Solving for variable 'x'.

Reorder the terms:
7 + -6x + -1x + 3x2 = -7 + x + 7 + -1x

Combine like terms: -6x + -1x = -7x
7 + -7x + 3x2 = -7 + x + 7 + -1x

Reorder the terms:
7 + -7x + 3x2 = -7 + 7 + x + -1x

Combine like terms: -7 + 7 = 0
7 + -7x + 3x2 = 0 + x + -1x
7 + -7x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
7 + -7x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -2.333333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -2.333333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + -2.333333333
-2.333333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-2.333333333x + x2 = -2.333333333

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -2.333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -2.333333333 + 1.361111112

Combine like terms: -2.333333333 + 1.361111112 = -0.972222221
1.361111112 + -2.333333333x + x2 = -0.972222221

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -0.972222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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