3(x-4)(x-4)+27=0

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Solution for 3(x-4)(x-4)+27=0 equation: 


Simplifying
3(x + -4)(x + -4) + 27 = 0

Reorder the terms:
3(-4 + x)(x + -4) + 27 = 0

Reorder the terms:
3(-4 + x)(-4 + x) + 27 = 0

Multiply (-4 + x) * (-4 + x)
3(-4(-4 + x) + x(-4 + x)) + 27 = 0
3((-4 * -4 + x * -4) + x(-4 + x)) + 27 = 0
3((16 + -4x) + x(-4 + x)) + 27 = 0
3(16 + -4x + (-4 * x + x * x)) + 27 = 0
3(16 + -4x + (-4x + x2)) + 27 = 0

Combine like terms: -4x + -4x = -8x
3(16 + -8x + x2) + 27 = 0
(16 * 3 + -8x * 3 + x2 * 3) + 27 = 0
(48 + -24x + 3x2) + 27 = 0

Reorder the terms:
48 + 27 + -24x + 3x2 = 0

Combine like terms: 48 + 27 = 75
75 + -24x + 3x2 = 0

Solving
75 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(25 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
25 + -8x + x2 = 0

Solving
25 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -8x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -8x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -8x + x2 = 0 + -25
-8x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-8x + x2 = -25

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -25 + 16

Reorder the terms:
16 + -8x + x2 = -25 + 16

Combine like terms: -25 + 16 = -9
16 + -8x + x2 = -9

Factor a perfect square on the left side:
(x + -4)(x + -4) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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