y^2-18y=199

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Solution for y^2-18y=199 equation:


Simplifying
y2 + -18y = 199

Reorder the terms:
-18y + y2 = 199

Solving
-18y + y2 = 199

Solving for variable 'y'.

Reorder the terms:
-199 + -18y + y2 = 199 + -199

Combine like terms: 199 + -199 = 0
-199 + -18y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '199' to each side of the equation.
-199 + -18y + 199 + y2 = 0 + 199

Reorder the terms:
-199 + 199 + -18y + y2 = 0 + 199

Combine like terms: -199 + 199 = 0
0 + -18y + y2 = 0 + 199
-18y + y2 = 0 + 199

Combine like terms: 0 + 199 = 199
-18y + y2 = 199

The y term is -18y.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18y + 81 + y2 = 199 + 81

Reorder the terms:
81 + -18y + y2 = 199 + 81

Combine like terms: 199 + 81 = 280
81 + -18y + y2 = 280

Factor a perfect square on the left side:
(y + -9)(y + -9) = 280

Calculate the square root of the right side: 16.733200531

Break this problem into two subproblems by setting 
(y + -9) equal to 16.733200531 and -16.733200531.

Subproblem 1

y + -9 = 16.733200531 Simplifying y + -9 = 16.733200531 Reorder the terms: -9 + y = 16.733200531 Solving -9 + y = 16.733200531 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 16.733200531 + 9 Combine like terms: -9 + 9 = 0 0 + y = 16.733200531 + 9 y = 16.733200531 + 9 Combine like terms: 16.733200531 + 9 = 25.733200531 y = 25.733200531 Simplifying y = 25.733200531

Subproblem 2

y + -9 = -16.733200531 Simplifying y + -9 = -16.733200531 Reorder the terms: -9 + y = -16.733200531 Solving -9 + y = -16.733200531 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -16.733200531 + 9 Combine like terms: -9 + 9 = 0 0 + y = -16.733200531 + 9 y = -16.733200531 + 9 Combine like terms: -16.733200531 + 9 = -7.733200531 y = -7.733200531 Simplifying y = -7.733200531

Solution

The solution to the problem is based on the solutions from the subproblems. y = {25.733200531, -7.733200531}

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