1=a^2+1.083a^2+1.57a^2

Solution for 1=a^2+1.083a^2+1.57a^2 equation:

Simplifying
1 = a2 + 1.083a2 + 1.57a2

Combine like terms: a2 + 1.083a2 = 2.083a2
1 = 2.083a2 + 1.57a2

Combine like terms: 2.083a2 + 1.57a2 = 3.653a2
1 = 3.653a2

Solving
1 = 3.653a2

Solving for variable 'a'.

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

Add '-3.653a2' to each side of the equation.
1 + -3.653a2 = 3.653a2 + -3.653a2

Combine like terms: 3.653a2 + -3.653a2 = 0.000
1 + -3.653a2 = 0.000

Add '-1' to each side of the equation.
1 + -1 + -3.653a2 = 0.000 + -1

Combine like terms: 1 + -1 = 0
0 + -3.653a2 = 0.000 + -1
-3.653a2 = 0.000 + -1

Combine like terms: 0.000 + -1 = -1
-3.653a2 = -1

Divide each side by '-3.653'.
a2 = 0.2737476047

Simplifying
a2 = 0.2737476047

Take the square root of each side:
a = {-0.523208949, 0.523208949}