7+(X-4)(X-4)=11

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Solution for 7+(X-4)(X-4)=11 equation: 


Simplifying
7 + (X + -4)(X + -4) = 11

Reorder the terms:
7 + (-4 + X)(X + -4) = 11

Reorder the terms:
7 + (-4 + X)(-4 + X) = 11

Multiply (-4 + X) * (-4 + X)
7 + (-4(-4 + X) + X(-4 + X)) = 11
7 + ((-4 * -4 + X * -4) + X(-4 + X)) = 11
7 + ((16 + -4X) + X(-4 + X)) = 11
7 + (16 + -4X + (-4 * X + X * X)) = 11
7 + (16 + -4X + (-4X + X2)) = 11

Combine like terms: -4X + -4X = -8X
7 + (16 + -8X + X2) = 11

Combine like terms: 7 + 16 = 23
23 + -8X + X2 = 11

Solving
23 + -8X + X2 = 11

Solving for variable 'X'.

Reorder the terms:
23 + -11 + -8X + X2 = 11 + -11

Combine like terms: 23 + -11 = 12
12 + -8X + X2 = 11 + -11

Combine like terms: 11 + -11 = 0
12 + -8X + X2 = 0

Factor a trinomial.
(2 + -1X)(6 + -1X) = 0


Subproblem 1
Set the factor '(2 + -1X)' equal to zero and attempt to solve:

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2

Subproblem 2
Set the factor '(6 + -1X)' equal to zero and attempt to solve:

Simplifying
6 + -1X = 0

Solving
6 + -1X = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1X = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X = 0 + -6
-1X = 0 + -6

Combine like terms: 0 + -6 = -6
-1X = -6

Divide each side by '-1'.
X = 6

Simplifying
X = 6
Solution
X = {2, 6}

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