4y^2-24y+9=0

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Solution for 4y^2-24y+9=0 equation:


Simplifying
4y2 + -24y + 9 = 0

Reorder the terms:
9 + -24y + 4y2 = 0

Solving
9 + -24y + 4y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
2.25 + -6y + y2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -6y + -2.25 + y2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -6y + y2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -6y + y2 = 0 + -2.25
-6y + y2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-6y + y2 = -2.25

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = -2.25 + 9

Reorder the terms:
9 + -6y + y2 = -2.25 + 9

Combine like terms: -2.25 + 9 = 6.75
9 + -6y + y2 = 6.75

Factor a perfect square on the left side:
(y + -3)(y + -3) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(y + -3) equal to 2.598076211 and -2.598076211.

Subproblem 1

y + -3 = 2.598076211 Simplifying y + -3 = 2.598076211 Reorder the terms: -3 + y = 2.598076211 Solving -3 + y = 2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.598076211 + 3 y = 2.598076211 + 3 Combine like terms: 2.598076211 + 3 = 5.598076211 y = 5.598076211 Simplifying y = 5.598076211

Subproblem 2

y + -3 = -2.598076211 Simplifying y + -3 = -2.598076211 Reorder the terms: -3 + y = -2.598076211 Solving -3 + y = -2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.598076211 + 3 y = -2.598076211 + 3 Combine like terms: -2.598076211 + 3 = 0.401923789 y = 0.401923789 Simplifying y = 0.401923789

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.598076211, 0.401923789}

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