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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