2y^2-8y+15-13y^2-8y+1=

Solution for 2y^2-8y+15-13y^2-8y+1= equation:

Simplifying
2y2 + -8y + 15 + -13y2 + -8y + 1 = 0

Reorder the terms:
15 + 1 + -8y + -8y + 2y2 + -13y2 = 0

Combine like terms: 15 + 1 = 16
16 + -8y + -8y + 2y2 + -13y2 = 0

Combine like terms: -8y + -8y = -16y
16 + -16y + 2y2 + -13y2 = 0

Combine like terms: 2y2 + -13y2 = -11y2
16 + -16y + -11y2 = 0

Solving
16 + -16y + -11y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-1.454545455 + 1.454545455y + y2 = 0

Move the constant term to the right:

Add '1.454545455' to each side of the equation.
-1.454545455 + 1.454545455y + 1.454545455 + y2 = 0 + 1.454545455

Reorder the terms:
-1.454545455 + 1.454545455 + 1.454545455y + y2 = 0 + 1.454545455

Combine like terms: -1.454545455 + 1.454545455 = 0.000000000
0.000000000 + 1.454545455y + y2 = 0 + 1.454545455
1.454545455y + y2 = 0 + 1.454545455

Combine like terms: 0 + 1.454545455 = 1.454545455
1.454545455y + y2 = 1.454545455

The y term is 1.454545455y.  Take half its coefficient (0.7272727275).
Square it (0.5289256202) and add it to both sides.

Add '0.5289256202' to each side of the equation.
1.454545455y + 0.5289256202 + y2 = 1.454545455 + 0.5289256202

Reorder the terms:
0.5289256202 + 1.454545455y + y2 = 1.454545455 + 0.5289256202

Combine like terms: 1.454545455 + 0.5289256202 = 1.9834710752
0.5289256202 + 1.454545455y + y2 = 1.9834710752

Factor a perfect square on the left side:
(y + 0.7272727275)(y + 0.7272727275) = 1.9834710752

Calculate the square root of the right side: 1.408357581

Break this problem into two subproblems by setting 
(y + 0.7272727275) equal to 1.408357581 and -1.408357581.

Subproblem 1
y + 0.7272727275 = 1.408357581

Simplifying
y + 0.7272727275 = 1.408357581

Reorder the terms:
0.7272727275 + y = 1.408357581

Solving
0.7272727275 + y = 1.408357581

Solving for variable 'y'.

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

Add '-0.7272727275' to each side of the equation.
0.7272727275 + -0.7272727275 + y = 1.408357581 + -0.7272727275

Combine like terms: 0.7272727275 + -0.7272727275 = 0.0000000000
0.0000000000 + y = 1.408357581 + -0.7272727275
y = 1.408357581 + -0.7272727275

Combine like terms: 1.408357581 + -0.7272727275 = 0.6810848535
y = 0.6810848535

Simplifying
y = 0.6810848535

Subproblem 2
y + 0.7272727275 = -1.408357581

Simplifying
y + 0.7272727275 = -1.408357581

Reorder the terms:
0.7272727275 + y = -1.408357581

Solving
0.7272727275 + y = -1.408357581

Solving for variable 'y'.

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

Add '-0.7272727275' to each side of the equation.
0.7272727275 + -0.7272727275 + y = -1.408357581 + -0.7272727275

Combine like terms: 0.7272727275 + -0.7272727275 = 0.0000000000
0.0000000000 + y = -1.408357581 + -0.7272727275
y = -1.408357581 + -0.7272727275

Combine like terms: -1.408357581 + -0.7272727275 = -2.1356303085
y = -2.1356303085

Simplifying
y = -2.1356303085

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.6810848535, -2.1356303085}