Y^2-45Y+30=0

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Solution for Y^2-45Y+30=0 equation:


Simplifying
Y2 + -45Y + 30 = 0

Reorder the terms:
30 + -45Y + Y2 = 0

Solving
30 + -45Y + Y2 = 0

Solving for variable 'Y'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -45Y + -30 + Y2 = 0 + -30

Reorder the terms:
30 + -30 + -45Y + Y2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -45Y + Y2 = 0 + -30
-45Y + Y2 = 0 + -30

Combine like terms: 0 + -30 = -30
-45Y + Y2 = -30

The Y term is -45Y.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45Y + 506.25 + Y2 = -30 + 506.25

Reorder the terms:
506.25 + -45Y + Y2 = -30 + 506.25

Combine like terms: -30 + 506.25 = 476.25
506.25 + -45Y + Y2 = 476.25

Factor a perfect square on the left side:
(Y + -22.5)(Y + -22.5) = 476.25

Calculate the square root of the right side: 21.823152843

Break this problem into two subproblems by setting 
(Y + -22.5) equal to 21.823152843 and -21.823152843.

Subproblem 1

Y + -22.5 = 21.823152843 Simplifying Y + -22.5 = 21.823152843 Reorder the terms: -22.5 + Y = 21.823152843 Solving -22.5 + Y = 21.823152843 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + Y = 21.823152843 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + Y = 21.823152843 + 22.5 Y = 21.823152843 + 22.5 Combine like terms: 21.823152843 + 22.5 = 44.323152843 Y = 44.323152843 Simplifying Y = 44.323152843

Subproblem 2

Y + -22.5 = -21.823152843 Simplifying Y + -22.5 = -21.823152843 Reorder the terms: -22.5 + Y = -21.823152843 Solving -22.5 + Y = -21.823152843 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + Y = -21.823152843 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + Y = -21.823152843 + 22.5 Y = -21.823152843 + 22.5 Combine like terms: -21.823152843 + 22.5 = 0.676847157 Y = 0.676847157 Simplifying Y = 0.676847157

Solution

The solution to the problem is based on the solutions from the subproblems. Y = {44.323152843, 0.676847157}

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