16z^2+-1=25z^2+-14z+2

Solution for 16z^2+-1=25z^2+-14z+2 equation:

Simplifying
16z2 + -1 = 25z2 + -14z + 2

Reorder the terms:
-1 + 16z2 = 25z2 + -14z + 2

Reorder the terms:
-1 + 16z2 = 2 + -14z + 25z2

Solving
-1 + 16z2 = 2 + -14z + 25z2

Solving for variable 'z'.

Reorder the terms:
-1 + -2 + 14z + 16z2 + -25z2 = 2 + -14z + 25z2 + -2 + 14z + -25z2

Combine like terms: -1 + -2 = -3
-3 + 14z + 16z2 + -25z2 = 2 + -14z + 25z2 + -2 + 14z + -25z2

Combine like terms: 16z2 + -25z2 = -9z2
-3 + 14z + -9z2 = 2 + -14z + 25z2 + -2 + 14z + -25z2

Reorder the terms:
-3 + 14z + -9z2 = 2 + -2 + -14z + 14z + 25z2 + -25z2

Combine like terms: 2 + -2 = 0
-3 + 14z + -9z2 = 0 + -14z + 14z + 25z2 + -25z2
-3 + 14z + -9z2 = -14z + 14z + 25z2 + -25z2

Combine like terms: -14z + 14z = 0
-3 + 14z + -9z2 = 0 + 25z2 + -25z2
-3 + 14z + -9z2 = 25z2 + -25z2

Combine like terms: 25z2 + -25z2 = 0
-3 + 14z + -9z2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
0.3333333333 + -1.555555556z + z2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.555555556z + -0.3333333333 + z2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.555555556z + z2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.555555556z + z2 = 0 + -0.3333333333
-1.555555556z + z2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.555555556z + z2 = -0.3333333333

The z term is -1.555555556z.  Take half its coefficient (-0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
-1.555555556z + 0.6049382720 + z2 = -0.3333333333 + 0.6049382720

Reorder the terms:
0.6049382720 + -1.555555556z + z2 = -0.3333333333 + 0.6049382720

Combine like terms: -0.3333333333 + 0.6049382720 = 0.2716049387
0.6049382720 + -1.555555556z + z2 = 0.2716049387

Factor a perfect square on the left side:
(z + -0.777777778)(z + -0.777777778) = 0.2716049387

Calculate the square root of the right side: 0.521157307

Break this problem into two subproblems by setting 
(z + -0.777777778) equal to 0.521157307 and -0.521157307.

Subproblem 1
z + -0.777777778 = 0.521157307

Simplifying
z + -0.777777778 = 0.521157307

Reorder the terms:
-0.777777778 + z = 0.521157307

Solving
-0.777777778 + z = 0.521157307

Solving for variable 'z'.

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

Add '0.777777778' to each side of the equation.
-0.777777778 + 0.777777778 + z = 0.521157307 + 0.777777778

Combine like terms: -0.777777778 + 0.777777778 = 0.000000000
0.000000000 + z = 0.521157307 + 0.777777778
z = 0.521157307 + 0.777777778

Combine like terms: 0.521157307 + 0.777777778 = 1.298935085
z = 1.298935085

Simplifying
z = 1.298935085

Subproblem 2
z + -0.777777778 = -0.521157307

Simplifying
z + -0.777777778 = -0.521157307

Reorder the terms:
-0.777777778 + z = -0.521157307

Solving
-0.777777778 + z = -0.521157307

Solving for variable 'z'.

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

Add '0.777777778' to each side of the equation.
-0.777777778 + 0.777777778 + z = -0.521157307 + 0.777777778

Combine like terms: -0.777777778 + 0.777777778 = 0.000000000
0.000000000 + z = -0.521157307 + 0.777777778
z = -0.521157307 + 0.777777778

Combine like terms: -0.521157307 + 0.777777778 = 0.256620471
z = 0.256620471

Simplifying
z = 0.256620471

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.298935085, 0.256620471}