y^2-3y+1=0

Simple and best practice solution for y^2-3y+1=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^2-3y+1=0 equation:


Simplifying
y2 + -3y + 1 = 0

Reorder the terms:
1 + -3y + y2 = 0

Solving
1 + -3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -3y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y + y2 = 0 + -1
-3y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3y + y2 = -1

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -1 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3y + y2 = 1.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

y + -1.5 = 1.118033989 Simplifying y + -1.5 = 1.118033989 Reorder the terms: -1.5 + y = 1.118033989 Solving -1.5 + y = 1.118033989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.118033989 + 1.5 y = 1.118033989 + 1.5 Combine like terms: 1.118033989 + 1.5 = 2.618033989 y = 2.618033989 Simplifying y = 2.618033989

Subproblem 2

y + -1.5 = -1.118033989 Simplifying y + -1.5 = -1.118033989 Reorder the terms: -1.5 + y = -1.118033989 Solving -1.5 + y = -1.118033989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.118033989 + 1.5 y = -1.118033989 + 1.5 Combine like terms: -1.118033989 + 1.5 = 0.381966011 y = 0.381966011 Simplifying y = 0.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.618033989, 0.381966011}

See similar equations:

| 5-3x+5x=29 | | 5=z+15 | | .05*a+7.50=.08*a | | 5y+2=78 | | 11+3(3y+6)= | | 14=5x+x-10 | | w+73=152 | | 10x+6=7x+6 | | 152=w+73 | | x-3(x+1)-2(x-1)=3 | | 6y+27=3(y-42) | | 9x-8x-48=2x-84 | | -3+2x-6x=-31 | | -19=28-k/16 | | 2t+9=7t | | -14=2x+x-5 | | Q^2+10Q+22=0 | | -4(x+6)=-4 | | 3+9x=x-10x | | 4c+(c-2)=-34 | | 2x^2-20x=288 | | z-42=-28 | | x+3+4x=58 | | 4x^2+8x-10=0 | | 6m-7-4-16=-23 | | 5x+10+7x=22 | | 2k+1=15 | | 2(c)+2(c)+16=72 | | 8q+17=4(3+2q) | | 3z^2-300=0 | | 3x+y=464 | | (2+x)+(5+(2+x))=180 |

Equations solver categories