2x^2+16x+64=1296

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Solution for 2x^2+16x+64=1296 equation: 


Simplifying
2x2 + 16x + 64 = 1296

Reorder the terms:
64 + 16x + 2x2 = 1296

Solving
64 + 16x + 2x2 = 1296

Solving for variable 'x'.

Reorder the terms:
64 + -1296 + 16x + 2x2 = 1296 + -1296

Combine like terms: 64 + -1296 = -1232
-1232 + 16x + 2x2 = 1296 + -1296

Combine like terms: 1296 + -1296 = 0
-1232 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-616 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-616 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-616 + 8x + x2 = 0

Solving
-616 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '616' to each side of the equation.
-616 + 8x + 616 + x2 = 0 + 616

Reorder the terms:
-616 + 616 + 8x + x2 = 0 + 616

Combine like terms: -616 + 616 = 0
0 + 8x + x2 = 0 + 616
8x + x2 = 0 + 616

Combine like terms: 0 + 616 = 616
8x + x2 = 616

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 = 616 + 16

Reorder the terms:
16 + 8x + x2 = 616 + 16

Combine like terms: 616 + 16 = 632
16 + 8x + x2 = 632

Factor a perfect square on the left side:
(x + 4)(x + 4) = 632

Calculate the square root of the right side: 25.13961018

Break this problem into two subproblems by setting 
(x + 4) equal to 25.13961018 and -25.13961018.


Subproblem 1
x + 4 = 25.13961018

Simplifying
x + 4 = 25.13961018

Reorder the terms:
4 + x = 25.13961018

Solving
4 + x = 25.13961018

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 = 25.13961018 + -4

Combine like terms: 4 + -4 = 0
0 + x = 25.13961018 + -4
x = 25.13961018 + -4

Combine like terms: 25.13961018 + -4 = 21.13961018
x = 21.13961018

Simplifying
x = 21.13961018


Subproblem 2
x + 4 = -25.13961018

Simplifying
x + 4 = -25.13961018

Reorder the terms:
4 + x = -25.13961018

Solving
4 + x = -25.13961018

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 = -25.13961018 + -4

Combine like terms: 4 + -4 = 0
0 + x = -25.13961018 + -4
x = -25.13961018 + -4

Combine like terms: -25.13961018 + -4 = -29.13961018
x = -29.13961018

Simplifying
x = -29.13961018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.13961018, -29.13961018}
Solution
x = {21.13961018, -29.13961018}

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