y^2-15y+49=0

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Solution for y^2-15y+49=0 equation: 


Simplifying
y2 + -15y + 49 = 0

Reorder the terms:
49 + -15y + y2 = 0

Solving
49 + -15y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -15y + -49 + y2 = 0 + -49

Reorder the terms:
49 + -49 + -15y + y2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -15y + y2 = 0 + -49
-15y + y2 = 0 + -49

Combine like terms: 0 + -49 = -49
-15y + y2 = -49

The y term is -15y.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15y + 56.25 + y2 = -49 + 56.25

Reorder the terms:
56.25 + -15y + y2 = -49 + 56.25

Combine like terms: -49 + 56.25 = 7.25
56.25 + -15y + y2 = 7.25

Factor a perfect square on the left side:
(y + -7.5)(y + -7.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(y + -7.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
y + -7.5 = 2.692582404

Simplifying
y + -7.5 = 2.692582404

Reorder the terms:
-7.5 + y = 2.692582404

Solving
-7.5 + y = 2.692582404

Solving for variable 'y'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + y = 2.692582404 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y = 2.692582404 + 7.5
y = 2.692582404 + 7.5

Combine like terms: 2.692582404 + 7.5 = 10.192582404
y = 10.192582404

Simplifying
y = 10.192582404


Subproblem 2
y + -7.5 = -2.692582404

Simplifying
y + -7.5 = -2.692582404

Reorder the terms:
-7.5 + y = -2.692582404

Solving
-7.5 + y = -2.692582404

Solving for variable 'y'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + y = -2.692582404 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y = -2.692582404 + 7.5
y = -2.692582404 + 7.5

Combine like terms: -2.692582404 + 7.5 = 4.807417596
y = 4.807417596

Simplifying
y = 4.807417596


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.192582404, 4.807417596}

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