y^2-5y+2=0

Simple and best practice solution for y^2-5y+2=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for y^2-5y+2=0 equation: 


Simplifying
y2 + -5y + 2 = 0

Reorder the terms:
2 + -5y + y2 = 0

Solving
2 + -5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -5y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y + y2 = 0 + -2
-5y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5y + y2 = -2

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -2 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5y + y2 = 4.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(y + -2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
y + -2.5 = 2.061552813

Simplifying
y + -2.5 = 2.061552813

Reorder the terms:
-2.5 + y = 2.061552813

Solving
-2.5 + y = 2.061552813

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 2.061552813 + 2.5
y = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
y = 4.561552813

Simplifying
y = 4.561552813


Subproblem 2
y + -2.5 = -2.061552813

Simplifying
y + -2.5 = -2.061552813

Reorder the terms:
-2.5 + y = -2.061552813

Solving
-2.5 + y = -2.061552813

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -2.061552813 + 2.5
y = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
y = 0.438447187

Simplifying
y = 0.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.561552813, 0.438447187}

See similar equations:

| 7x(-13+3x)+12=13 | | (x-9)(2x+3)=0 | | -3w+6-1=2 | | 7x-2=-4x+13 | | 3x-(5-2)+24=-1 | | -7r-5=-6 | | 2z-4-z=9 | | 3x-3y=-3 | | -5w-4=-2 | | 6+3t=8t-4 | | x-2y=-4 | | 3(2-2h)-2h=7h+13 | | 6x-2=16x-102 | | 4x^3-18x^2+20x=0 | | 2n-9=-5 | | 9x+12=-6 | | 5d+4=4+d | | -448=64g | | 55-6x=3x+15 | | 12u-8=-8 | | -18-9x=9x+18 | | -87-7x=10x+15 | | 3x+9=-63-9x | | 14-5n=3m | | 5-6x=12-7x | | 105-6x=2x+17 | | 3a-4b=21 | | -7g+24=-39 | | -4x-5y=9 | | 4x-5y=9 | | 66-2x=10x+18 | | 3x-4=12x-85 |

Equations solver categories