y^2-10y+5=0

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Solution for y^2-10y+5=0 equation:


Simplifying
y2 + -10y + 5 = 0

Reorder the terms:
5 + -10y + y2 = 0

Solving
5 + -10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -10y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10y + y2 = 0 + -5
-10y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-10y + y2 = -5

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 = -5 + 25

Reorder the terms:
25 + -10y + y2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + -10y + y2 = 20

Factor a perfect square on the left side:
(y + -5)(y + -5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + -5) equal to 4.472135955 and -4.472135955.

Subproblem 1

y + -5 = 4.472135955 Simplifying y + -5 = 4.472135955 Reorder the terms: -5 + y = 4.472135955 Solving -5 + y = 4.472135955 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 = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.472135955 + 5 y = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 y = 9.472135955 Simplifying y = 9.472135955

Subproblem 2

y + -5 = -4.472135955 Simplifying y + -5 = -4.472135955 Reorder the terms: -5 + y = -4.472135955 Solving -5 + y = -4.472135955 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 = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.472135955 + 5 y = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 y = 0.527864045 Simplifying y = 0.527864045

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.472135955, 0.527864045}

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