y^2-28y+3=0

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Solution for y^2-28y+3=0 equation:


Simplifying
y2 + -28y + 3 = 0

Reorder the terms:
3 + -28y + y2 = 0

Solving
3 + -28y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -28y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -28y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -28y + y2 = 0 + -3
-28y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-28y + y2 = -3

The y term is -28y.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28y + 196 + y2 = -3 + 196

Reorder the terms:
196 + -28y + y2 = -3 + 196

Combine like terms: -3 + 196 = 193
196 + -28y + y2 = 193

Factor a perfect square on the left side:
(y + -14)(y + -14) = 193

Calculate the square root of the right side: 13.892443989

Break this problem into two subproblems by setting 
(y + -14) equal to 13.892443989 and -13.892443989.

Subproblem 1

y + -14 = 13.892443989 Simplifying y + -14 = 13.892443989 Reorder the terms: -14 + y = 13.892443989 Solving -14 + y = 13.892443989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + y = 13.892443989 + 14 Combine like terms: -14 + 14 = 0 0 + y = 13.892443989 + 14 y = 13.892443989 + 14 Combine like terms: 13.892443989 + 14 = 27.892443989 y = 27.892443989 Simplifying y = 27.892443989

Subproblem 2

y + -14 = -13.892443989 Simplifying y + -14 = -13.892443989 Reorder the terms: -14 + y = -13.892443989 Solving -14 + y = -13.892443989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + y = -13.892443989 + 14 Combine like terms: -14 + 14 = 0 0 + y = -13.892443989 + 14 y = -13.892443989 + 14 Combine like terms: -13.892443989 + 14 = 0.107556011 y = 0.107556011 Simplifying y = 0.107556011

Solution

The solution to the problem is based on the solutions from the subproblems. y = {27.892443989, 0.107556011}

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