2x^2-16x+64=200

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Solution for 2x^2-16x+64=200 equation: 


Simplifying
2x2 + -16x + 64 = 200

Reorder the terms:
64 + -16x + 2x2 = 200

Solving
64 + -16x + 2x2 = 200

Solving for variable 'x'.

Reorder the terms:
64 + -200 + -16x + 2x2 = 200 + -200

Combine like terms: 64 + -200 = -136
-136 + -16x + 2x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-136 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + -8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-68 + -8x + x2 = 0

Solving
-68 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + -8x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + -8x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -8x + x2 = 0 + 68
-8x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
-8x + x2 = 68

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 = 68 + 16

Reorder the terms:
16 + -8x + x2 = 68 + 16

Combine like terms: 68 + 16 = 84
16 + -8x + x2 = 84

Factor a perfect square on the left side:
(x + -4)(x + -4) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + -4) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + -4 = 9.16515139

Simplifying
x + -4 = 9.16515139

Reorder the terms:
-4 + x = 9.16515139

Solving
-4 + x = 9.16515139

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 9.16515139 + 4

Combine like terms: -4 + 4 = 0
0 + x = 9.16515139 + 4
x = 9.16515139 + 4

Combine like terms: 9.16515139 + 4 = 13.16515139
x = 13.16515139

Simplifying
x = 13.16515139


Subproblem 2
x + -4 = -9.16515139

Simplifying
x + -4 = -9.16515139

Reorder the terms:
-4 + x = -9.16515139

Solving
-4 + x = -9.16515139

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -9.16515139 + 4

Combine like terms: -4 + 4 = 0
0 + x = -9.16515139 + 4
x = -9.16515139 + 4

Combine like terms: -9.16515139 + 4 = -5.16515139
x = -5.16515139

Simplifying
x = -5.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.16515139, -5.16515139}
Solution
x = {13.16515139, -5.16515139}

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