y^2=10y-18

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Solution for y^2=10y-18 equation:


Simplifying
y2 = 10y + -18

Reorder the terms:
y2 = -18 + 10y

Solving
y2 = -18 + 10y

Solving for variable 'y'.

Reorder the terms:
18 + -10y + y2 = -18 + 10y + 18 + -10y

Reorder the terms:
18 + -10y + y2 = -18 + 18 + 10y + -10y

Combine like terms: -18 + 18 = 0
18 + -10y + y2 = 0 + 10y + -10y
18 + -10y + y2 = 10y + -10y

Combine like terms: 10y + -10y = 0
18 + -10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10y + -18 + y2 = 0 + -18

Reorder the terms:
18 + -18 + -10y + y2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10y + y2 = 0 + -18
-10y + y2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10y + y2 = -18

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 = -18 + 25

Reorder the terms:
25 + -10y + y2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10y + y2 = 7

Factor a perfect square on the left side:
(y + -5)(y + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -5) equal to 2.645751311 and -2.645751311.

Subproblem 1

y + -5 = 2.645751311 Simplifying y + -5 = 2.645751311 Reorder the terms: -5 + y = 2.645751311 Solving -5 + y = 2.645751311 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 = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + y = 2.645751311 + 5 y = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 y = 7.645751311 Simplifying y = 7.645751311

Subproblem 2

y + -5 = -2.645751311 Simplifying y + -5 = -2.645751311 Reorder the terms: -5 + y = -2.645751311 Solving -5 + y = -2.645751311 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 = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + y = -2.645751311 + 5 y = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 y = 2.354248689 Simplifying y = 2.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.645751311, 2.354248689}

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