4y^2-28y+9=0

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Solution for 4y^2-28y+9=0 equation:


Simplifying
4y2 + -28y + 9 = 0

Reorder the terms:
9 + -28y + 4y2 = 0

Solving
9 + -28y + 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 + -7y + y2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -7y + -2.25 + y2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -7y + y2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -7y + y2 = 0 + -2.25
-7y + y2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-7y + y2 = -2.25

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -2.25 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -2.25 + 12.25

Combine like terms: -2.25 + 12.25 = 10
12.25 + -7y + y2 = 10

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(y + -3.5) equal to 3.16227766 and -3.16227766.

Subproblem 1

y + -3.5 = 3.16227766 Simplifying y + -3.5 = 3.16227766 Reorder the terms: -3.5 + y = 3.16227766 Solving -3.5 + y = 3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 3.16227766 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 3.16227766 + 3.5 y = 3.16227766 + 3.5 Combine like terms: 3.16227766 + 3.5 = 6.66227766 y = 6.66227766 Simplifying y = 6.66227766

Subproblem 2

y + -3.5 = -3.16227766 Simplifying y + -3.5 = -3.16227766 Reorder the terms: -3.5 + y = -3.16227766 Solving -3.5 + y = -3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -3.16227766 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -3.16227766 + 3.5 y = -3.16227766 + 3.5 Combine like terms: -3.16227766 + 3.5 = 0.33772234 y = 0.33772234 Simplifying y = 0.33772234

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.66227766, 0.33772234}

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