y^2-10y-38=0

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Solution for y^2-10y-38=0 equation: 


Simplifying
y2 + -10y + -38 = 0

Reorder the terms:
-38 + -10y + y2 = 0

Solving
-38 + -10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -10y + 38 + y2 = 0 + 38

Reorder the terms:
-38 + 38 + -10y + y2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -10y + y2 = 0 + 38
-10y + y2 = 0 + 38

Combine like terms: 0 + 38 = 38
-10y + y2 = 38

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = 38 + 25

Reorder the terms:
25 + -10y + y2 = 38 + 25

Combine like terms: 38 + 25 = 63
25 + -10y + y2 = 63

Factor a perfect square on the left side:
(y + -5)(y + -5) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(y + -5) equal to 7.937253933 and -7.937253933.


Subproblem 1
y + -5 = 7.937253933

Simplifying
y + -5 = 7.937253933

Reorder the terms:
-5 + y = 7.937253933

Solving
-5 + y = 7.937253933

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 7.937253933 + 5

Combine like terms: -5 + 5 = 0
0 + y = 7.937253933 + 5
y = 7.937253933 + 5

Combine like terms: 7.937253933 + 5 = 12.937253933
y = 12.937253933

Simplifying
y = 12.937253933


Subproblem 2
y + -5 = -7.937253933

Simplifying
y + -5 = -7.937253933

Reorder the terms:
-5 + y = -7.937253933

Solving
-5 + y = -7.937253933

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -7.937253933 + 5

Combine like terms: -5 + 5 = 0
0 + y = -7.937253933 + 5
y = -7.937253933 + 5

Combine like terms: -7.937253933 + 5 = -2.937253933
y = -2.937253933

Simplifying
y = -2.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.937253933, -2.937253933}

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