4y-y^2=2

Simple and best practice solution for 4y-y^2=2 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 4y-y^2=2 equation:


Simplifying
4y + -1y2 = 2

Solving
4y + -1y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 4y + -1y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 4y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -4y + y2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -4y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4y + y2 = 0 + -2
-4y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4y + y2 = -2

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -2 + 4

Reorder the terms:
4 + -4y + y2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4y + y2 = 2

Factor a perfect square on the left side:
(y + -2)(y + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + -2) equal to 1.414213562 and -1.414213562.

Subproblem 1

y + -2 = 1.414213562 Simplifying y + -2 = 1.414213562 Reorder the terms: -2 + y = 1.414213562 Solving -2 + y = 1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.414213562 + 2 y = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 y = 3.414213562 Simplifying y = 3.414213562

Subproblem 2

y + -2 = -1.414213562 Simplifying y + -2 = -1.414213562 Reorder the terms: -2 + y = -1.414213562 Solving -2 + y = -1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.414213562 + 2 y = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 y = 0.585786438 Simplifying y = 0.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.414213562, 0.585786438}

See similar equations:

| (2x-y)(X+3y)=0 | | (D^4+2D^3-2d^2)y=x^2+3e^2x+4sinx | | -1-3(5x-5)=134 | | 19-3x=8x+4 | | 22=4+g | | 5x+8-3x=10 | | 110=9k+38 | | x^2-mx-m^2-5=0 | | 2(x-5)=3(x-3) | | 110=pk+38 | | sin(1.5x)=0 | | 4.3y=43.4 | | tx^2+2x+2=0 | | X^2-0.22x+0.0121= | | -1.5x-4.56x=36 | | log(5x+8)=1+log(x-8) | | w^2+2w=20 | | 8-4v=12 | | 91=-9x+19 | | 5y^2+4y+1=29 | | H(t)=-16t+32t+110t | | (8x-20)+(110-8x)=90 | | -v+5=-3(v-1) | | (x+15)*y=(y+0.05)*x | | 9x-2+6=40 | | 5z-17=14 | | 15x-35=90 | | 5d+8=4d+12 | | 3(5x-6)=27 | | 2(x+6)+(x+2)=2x+8 | | (-5x+6)(6x+3)-(6x+3)=0 | | x*y=4.5 |

Equations solver categories