y^2-15y+5=

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Solution for y^2-15y+5= equation:


Simplifying
y2 + -15y + 5 = 0

Reorder the terms:
5 + -15y + y2 = 0

Solving
5 + -15y + 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 + -15y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -15y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -15y + y2 = 0 + -5
-15y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-15y + y2 = -5

The y term is -15y.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15y + 56.25 + y2 = -5 + 56.25

Reorder the terms:
56.25 + -15y + y2 = -5 + 56.25

Combine like terms: -5 + 56.25 = 51.25
56.25 + -15y + y2 = 51.25

Factor a perfect square on the left side:
(y + -7.5)(y + -7.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(y + -7.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

y + -7.5 = 7.158910532 Simplifying y + -7.5 = 7.158910532 Reorder the terms: -7.5 + y = 7.158910532 Solving -7.5 + y = 7.158910532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 7.158910532 + 7.5 y = 7.158910532 + 7.5 Combine like terms: 7.158910532 + 7.5 = 14.658910532 y = 14.658910532 Simplifying y = 14.658910532

Subproblem 2

y + -7.5 = -7.158910532 Simplifying y + -7.5 = -7.158910532 Reorder the terms: -7.5 + y = -7.158910532 Solving -7.5 + y = -7.158910532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -7.158910532 + 7.5 y = -7.158910532 + 7.5 Combine like terms: -7.158910532 + 7.5 = 0.341089468 y = 0.341089468 Simplifying y = 0.341089468

Solution

The solution to the problem is based on the solutions from the subproblems. y = {14.658910532, 0.341089468}

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