16(x^2-16x+49)=0

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Solution for 16(x^2-16x+49)=0 equation: 


Simplifying
16(x2 + -16x + 49) = 0

Reorder the terms:
16(49 + -16x + x2) = 0
(49 * 16 + -16x * 16 + x2 * 16) = 0
(784 + -256x + 16x2) = 0

Solving
784 + -256x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(49 + -16x + x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(49 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
49 + -16x + x2 = 0

Solving
49 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -16x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + -16x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -16x + x2 = 0 + -49
-16x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
-16x + x2 = -49

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -49 + 64

Reorder the terms:
64 + -16x + x2 = -49 + 64

Combine like terms: -49 + 64 = 15
64 + -16x + x2 = 15

Factor a perfect square on the left side:
(x + -8)(x + -8) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -8) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + -8 = 3.872983346

Simplifying
x + -8 = 3.872983346

Reorder the terms:
-8 + x = 3.872983346

Solving
-8 + x = 3.872983346

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 3.872983346 + 8

Combine like terms: -8 + 8 = 0
0 + x = 3.872983346 + 8
x = 3.872983346 + 8

Combine like terms: 3.872983346 + 8 = 11.872983346
x = 11.872983346

Simplifying
x = 11.872983346


Subproblem 2
x + -8 = -3.872983346

Simplifying
x + -8 = -3.872983346

Reorder the terms:
-8 + x = -3.872983346

Solving
-8 + x = -3.872983346

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -3.872983346 + 8

Combine like terms: -8 + 8 = 0
0 + x = -3.872983346 + 8
x = -3.872983346 + 8

Combine like terms: -3.872983346 + 8 = 4.127016654
x = 4.127016654

Simplifying
x = 4.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.872983346, 4.127016654}
Solution
x = {11.872983346, 4.127016654}

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