(x-5)*(x-1)+49=-51

Solution for (x-5)*(x-1)+49=-51 equation:

Simplifying
(x + -5)(x + -1) + 49 = -51

Reorder the terms:
(-5 + x)(x + -1) + 49 = -51

Reorder the terms:
(-5 + x)(-1 + x) + 49 = -51

Multiply (-5 + x) * (-1 + x)
(-5(-1 + x) + x(-1 + x)) + 49 = -51
((-1 * -5 + x * -5) + x(-1 + x)) + 49 = -51
((5 + -5x) + x(-1 + x)) + 49 = -51
(5 + -5x + (-1 * x + x * x)) + 49 = -51
(5 + -5x + (-1x + x2)) + 49 = -51

Combine like terms: -5x + -1x = -6x
(5 + -6x + x2) + 49 = -51

Reorder the terms:
5 + 49 + -6x + x2 = -51

Combine like terms: 5 + 49 = 54
54 + -6x + x2 = -51

Solving
54 + -6x + x2 = -51

Solving for variable 'x'.

Reorder the terms:
54 + 51 + -6x + x2 = -51 + 51

Combine like terms: 54 + 51 = 105
105 + -6x + x2 = -51 + 51

Combine like terms: -51 + 51 = 0
105 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-105' to each side of the equation.
105 + -6x + -105 + x2 = 0 + -105

Reorder the terms:
105 + -105 + -6x + x2 = 0 + -105

Combine like terms: 105 + -105 = 0
0 + -6x + x2 = 0 + -105
-6x + x2 = 0 + -105

Combine like terms: 0 + -105 = -105
-6x + x2 = -105

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -105 + 9

Reorder the terms:
9 + -6x + x2 = -105 + 9

Combine like terms: -105 + 9 = -96
9 + -6x + x2 = -96

Factor a perfect square on the left side:
(x + -3)(x + -3) = -96

Can't calculate square root of the right side.

The solution to this equation could not be determined.