8y+y^2=189

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Solution for 8y+y^2=189 equation:


Simplifying
8y + y2 = 189

Solving
8y + y2 = 189

Solving for variable 'y'.

Reorder the terms:
-189 + 8y + y2 = 189 + -189

Combine like terms: 189 + -189 = 0
-189 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '189' to each side of the equation.
-189 + 8y + 189 + y2 = 0 + 189

Reorder the terms:
-189 + 189 + 8y + y2 = 0 + 189

Combine like terms: -189 + 189 = 0
0 + 8y + y2 = 0 + 189
8y + y2 = 0 + 189

Combine like terms: 0 + 189 = 189
8y + y2 = 189

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 189 + 16

Reorder the terms:
16 + 8y + y2 = 189 + 16

Combine like terms: 189 + 16 = 205
16 + 8y + y2 = 205

Factor a perfect square on the left side:
(y + 4)(y + 4) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(y + 4) equal to 14.317821063 and -14.317821063.

Subproblem 1

y + 4 = 14.317821063 Simplifying y + 4 = 14.317821063 Reorder the terms: 4 + y = 14.317821063 Solving 4 + y = 14.317821063 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 14.317821063 + -4 Combine like terms: 4 + -4 = 0 0 + y = 14.317821063 + -4 y = 14.317821063 + -4 Combine like terms: 14.317821063 + -4 = 10.317821063 y = 10.317821063 Simplifying y = 10.317821063

Subproblem 2

y + 4 = -14.317821063 Simplifying y + 4 = -14.317821063 Reorder the terms: 4 + y = -14.317821063 Solving 4 + y = -14.317821063 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -14.317821063 + -4 Combine like terms: 4 + -4 = 0 0 + y = -14.317821063 + -4 y = -14.317821063 + -4 Combine like terms: -14.317821063 + -4 = -18.317821063 y = -18.317821063 Simplifying y = -18.317821063

Solution

The solution to the problem is based on the solutions from the subproblems. y = {10.317821063, -18.317821063}

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