x-6=x(x)-3x+4

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Solution for x-6=x(x)-3x+4 equation:


Simplifying
x + -6 = x(x) + -3x + 4

Reorder the terms:
-6 + x = x(x) + -3x + 4

Multiply x * x
-6 + x = x2 + -3x + 4

Reorder the terms:
-6 + x = 4 + -3x + x2

Solving
-6 + x = 4 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + -4 + x + 3x + -1x2 = 4 + -3x + x2 + -4 + 3x + -1x2

Combine like terms: -6 + -4 = -10
-10 + x + 3x + -1x2 = 4 + -3x + x2 + -4 + 3x + -1x2

Combine like terms: x + 3x = 4x
-10 + 4x + -1x2 = 4 + -3x + x2 + -4 + 3x + -1x2

Reorder the terms:
-10 + 4x + -1x2 = 4 + -4 + -3x + 3x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-10 + 4x + -1x2 = 0 + -3x + 3x + x2 + -1x2
-10 + 4x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-10 + 4x + -1x2 = 0 + x2 + -1x2
-10 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 4x + -1x2 = 0

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

Divide each side by '-1'.
10 + -4x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -4x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -4x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -4x + x2 = 0 + -10
-4x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-4x + x2 = -10

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -10 + 4

Reorder the terms:
4 + -4x + x2 = -10 + 4

Combine like terms: -10 + 4 = -6
4 + -4x + x2 = -6

Factor a perfect square on the left side:
(x + -2)(x + -2) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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