y^2-7y-176=0

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Solution for y^2-7y-176=0 equation: 


Simplifying
y2 + -7y + -176 = 0

Reorder the terms:
-176 + -7y + y2 = 0

Solving
-176 + -7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '176' to each side of the equation.
-176 + -7y + 176 + y2 = 0 + 176

Reorder the terms:
-176 + 176 + -7y + y2 = 0 + 176

Combine like terms: -176 + 176 = 0
0 + -7y + y2 = 0 + 176
-7y + y2 = 0 + 176

Combine like terms: 0 + 176 = 176
-7y + y2 = 176

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = 176 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 176 + 12.25

Combine like terms: 176 + 12.25 = 188.25
12.25 + -7y + y2 = 188.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 188.25

Calculate the square root of the right side: 13.720422734

Break this problem into two subproblems by setting 
(y + -3.5) equal to 13.720422734 and -13.720422734.


Subproblem 1
y + -3.5 = 13.720422734

Simplifying
y + -3.5 = 13.720422734

Reorder the terms:
-3.5 + y = 13.720422734

Solving
-3.5 + y = 13.720422734

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 13.720422734 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 13.720422734 + 3.5
y = 13.720422734 + 3.5

Combine like terms: 13.720422734 + 3.5 = 17.220422734
y = 17.220422734

Simplifying
y = 17.220422734


Subproblem 2
y + -3.5 = -13.720422734

Simplifying
y + -3.5 = -13.720422734

Reorder the terms:
-3.5 + y = -13.720422734

Solving
-3.5 + y = -13.720422734

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -13.720422734 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -13.720422734 + 3.5
y = -13.720422734 + 3.5

Combine like terms: -13.720422734 + 3.5 = -10.220422734
y = -10.220422734

Simplifying
y = -10.220422734


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.220422734, -10.220422734}

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