-4y^2+26y-25=0

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Solution for -4y^2+26y-25=0 equation: 


Simplifying
-4y2 + 26y + -25 = 0

Reorder the terms:
-25 + 26y + -4y2 = 0

Solving
-25 + 26y + -4y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
6.25 + -6.5y + y2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -6.5y + -6.25 + y2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -6.5y + y2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -6.5y + y2 = 0 + -6.25
-6.5y + y2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-6.5y + y2 = -6.25

The y term is -6.5y.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5y + 10.5625 + y2 = -6.25 + 10.5625

Reorder the terms:
10.5625 + -6.5y + y2 = -6.25 + 10.5625

Combine like terms: -6.25 + 10.5625 = 4.3125
10.5625 + -6.5y + y2 = 4.3125

Factor a perfect square on the left side:
(y + -3.25)(y + -3.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(y + -3.25) equal to 2.076655966 and -2.076655966.


Subproblem 1
y + -3.25 = 2.076655966

Simplifying
y + -3.25 = 2.076655966

Reorder the terms:
-3.25 + y = 2.076655966

Solving
-3.25 + y = 2.076655966

Solving for variable 'y'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + y = 2.076655966 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + y = 2.076655966 + 3.25
y = 2.076655966 + 3.25

Combine like terms: 2.076655966 + 3.25 = 5.326655966
y = 5.326655966

Simplifying
y = 5.326655966


Subproblem 2
y + -3.25 = -2.076655966

Simplifying
y + -3.25 = -2.076655966

Reorder the terms:
-3.25 + y = -2.076655966

Solving
-3.25 + y = -2.076655966

Solving for variable 'y'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + y = -2.076655966 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + y = -2.076655966 + 3.25
y = -2.076655966 + 3.25

Combine like terms: -2.076655966 + 3.25 = 1.173344034
y = 1.173344034

Simplifying
y = 1.173344034


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.326655966, 1.173344034}

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