1200=(a^2+64)*(a^2+144)

Solution for 1200=(a^2+64)*(a^2+144) equation:

Simplifying
1200 = (a2 + 64)(a2 + 144)

Reorder the terms:
1200 = (64 + a2)(a2 + 144)

Reorder the terms:
1200 = (64 + a2)(144 + a2)

Multiply (64 + a2) * (144 + a2)
1200 = (64(144 + a2) + a2(144 + a2))
1200 = ((144 * 64 + a2 * 64) + a2(144 + a2))
1200 = ((9216 + 64a2) + a2(144 + a2))
1200 = (9216 + 64a2 + (144 * a2 + a2 * a2))
1200 = (9216 + 64a2 + (144a2 + a4))

Combine like terms: 64a2 + 144a2 = 208a2
1200 = (9216 + 208a2 + a4)

Solving
1200 = 9216 + 208a2 + a4

Solving for variable 'a'.

Combine like terms: 1200 + -9216 = -8016
-8016 + -208a2 + -1a4 = 9216 + 208a2 + a4 + -9216 + -208a2 + -1a4

Reorder the terms:
-8016 + -208a2 + -1a4 = 9216 + -9216 + 208a2 + -208a2 + a4 + -1a4

Combine like terms: 9216 + -9216 = 0
-8016 + -208a2 + -1a4 = 0 + 208a2 + -208a2 + a4 + -1a4
-8016 + -208a2 + -1a4 = 208a2 + -208a2 + a4 + -1a4

Combine like terms: 208a2 + -208a2 = 0
-8016 + -208a2 + -1a4 = 0 + a4 + -1a4
-8016 + -208a2 + -1a4 = a4 + -1a4

Combine like terms: a4 + -1a4 = 0
-8016 + -208a2 + -1a4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8016 + 208a2 + a4) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8016 + 208a2 + a4)' equal to zero and attempt to solve:

Simplifying
8016 + 208a2 + a4 = 0

Solving
8016 + 208a2 + a4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8016' to each side of the equation.
8016 + 208a2 + -8016 + a4 = 0 + -8016

Reorder the terms:
8016 + -8016 + 208a2 + a4 = 0 + -8016

Combine like terms: 8016 + -8016 = 0
0 + 208a2 + a4 = 0 + -8016
208a2 + a4 = 0 + -8016

Combine like terms: 0 + -8016 = -8016
208a2 + a4 = -8016

The a term is 208a2.  Take half its coefficient (104).
Square it (10816) and add it to both sides.

Add '10816' to each side of the equation.
208a2 + 10816 + a4 = -8016 + 10816

Reorder the terms:
10816 + 208a2 + a4 = -8016 + 10816

Combine like terms: -8016 + 10816 = 2800
10816 + 208a2 + a4 = 2800

Factor a perfect square on the left side:
(a2 + 104)(a2 + 104) = 2800

Calculate the square root of the right side: 52.915026221

Break this problem into two subproblems by setting 
(a2 + 104) equal to 52.915026221 and -52.915026221.

Subproblem 1
a2 + 104 = 52.915026221

Simplifying
a2 + 104 = 52.915026221

Reorder the terms:
104 + a2 = 52.915026221

Solving
104 + a2 = 52.915026221

Solving for variable 'a'.

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

Add '-104' to each side of the equation.
104 + -104 + a2 = 52.915026221 + -104

Combine like terms: 104 + -104 = 0
0 + a2 = 52.915026221 + -104
a2 = 52.915026221 + -104

Combine like terms: 52.915026221 + -104 = -51.084973779
a2 = -51.084973779

Simplifying
a2 = -51.084973779

Reorder the terms:
51.084973779 + a2 = -51.084973779 + 51.084973779

Combine like terms: -51.084973779 + 51.084973779 = 0.000000000
51.084973779 + a2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2
a2 + 104 = -52.915026221

Simplifying
a2 + 104 = -52.915026221

Reorder the terms:
104 + a2 = -52.915026221

Solving
104 + a2 = -52.915026221

Solving for variable 'a'.

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

Add '-104' to each side of the equation.
104 + -104 + a2 = -52.915026221 + -104

Combine like terms: 104 + -104 = 0
0 + a2 = -52.915026221 + -104
a2 = -52.915026221 + -104

Combine like terms: -52.915026221 + -104 = -156.915026221
a2 = -156.915026221

Simplifying
a2 = -156.915026221

Reorder the terms:
156.915026221 + a2 = -156.915026221 + 156.915026221

Combine like terms: -156.915026221 + 156.915026221 = 0.000000000
156.915026221 + a2 = 0.000000000

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.

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

The solution to this equation could not be determined.