2y^2-4y=5

Simple and best practice solution for 2y^2-4y=5 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 2y^2-4y=5 equation:


Simplifying
2y2 + -4y = 5

Reorder the terms:
-4y + 2y2 = 5

Solving
-4y + 2y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + -4y + 2y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -4y + 2y2 = 0

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

Divide each side by '2'.
-2.5 + -2y + y2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2y + 2.5 + y2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2y + y2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2y + y2 = 0 + 2.5
-2y + y2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2y + y2 = 2.5

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 2.5 + 1

Reorder the terms:
1 + -2y + y2 = 2.5 + 1

Combine like terms: 2.5 + 1 = 3.5
1 + -2y + y2 = 3.5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(y + -1) equal to 1.870828693 and -1.870828693.

Subproblem 1

y + -1 = 1.870828693 Simplifying y + -1 = 1.870828693 Reorder the terms: -1 + y = 1.870828693 Solving -1 + y = 1.870828693 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.870828693 + 1 y = 1.870828693 + 1 Combine like terms: 1.870828693 + 1 = 2.870828693 y = 2.870828693 Simplifying y = 2.870828693

Subproblem 2

y + -1 = -1.870828693 Simplifying y + -1 = -1.870828693 Reorder the terms: -1 + y = -1.870828693 Solving -1 + y = -1.870828693 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.870828693 + 1 y = -1.870828693 + 1 Combine like terms: -1.870828693 + 1 = -0.870828693 y = -0.870828693 Simplifying y = -0.870828693

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.870828693, -0.870828693}

See similar equations:

| -11/20x=7 | | W^2+18w+80=0 | | 140x^2+340x=-120 | | 16n^2+24n+9= | | x+(x-3)+(x-6)=51 | | 30=-10t | | 300-6Q=1500+2Q^2 | | 8*x-3*x^2=0 | | 106/$2.00 | | .04(12)+.01t-.02(12+t)=0 | | 6=(-3)/5w | | 1/4b=15 | | x+(3+x)+(6+x)=51 | | 6(4x+11)= | | 6.7d=14.8 | | 2w+3=25 | | -16(x+6)=(x-64) | | (x-6)(5x+3)(3x-4)=0 | | -540.00+13.00x=180 | | x/58 | | sin37=x/20 | | 6p-3p+2p= | | -61=3x-5(-2x-6) | | 7=7-9c/10 | | x-.15x=75 | | -61=3x-5(2x-6) | | (6i)/(5-8i) | | w/2=14 | | -15t+5t=-33 | | (9(y-1))/4=-4y | | 2w+21=5w-3w-21 | | m-9=45 |

Equations solver categories