y^2-5y=3

Simple and best practice solution for y^2-5y=3 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=3 equation:


Simplifying
y2 + -5y = 3

Reorder the terms:
-5y + y2 = 3

Solving
-5y + y2 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + -5y + y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -5y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5y + y2 = 0 + 3
-5y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5y + y2 = 3

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 = 3 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5y + y2 = 9.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + -2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

y + -2.5 = 3.041381265 Simplifying y + -2.5 = 3.041381265 Reorder the terms: -2.5 + y = 3.041381265 Solving -2.5 + y = 3.041381265 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 = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 3.041381265 + 2.5 y = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 y = 5.541381265 Simplifying y = 5.541381265

Subproblem 2

y + -2.5 = -3.041381265 Simplifying y + -2.5 = -3.041381265 Reorder the terms: -2.5 + y = -3.041381265 Solving -2.5 + y = -3.041381265 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 = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -3.041381265 + 2.5 y = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 y = -0.541381265 Simplifying y = -0.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.541381265, -0.541381265}

See similar equations:

| -7n-4=-25 | | 29-(3y-1)=2(y-1)+3y | | -(x-1)=-4x-2 | | -5d+3=-12 | | 8-(x-2)=3x+4 | | 56=12+4n | | 3x^2=7x-2 | | x^2-14z+45=0 | | 3x+7=9x-5 | | x^2+26x+120=0 | | 6-4x=7x-9x+10-4 | | (-2n-1)=7 | | 2-x=11 | | (2x+5)-(5x+4)=6-2(x-3) | | 7-c=9 | | a-7-7=5 | | 5+4t=8 | | 13=9+4z | | -7-7=5 | | -2+3x=-(x+6) | | y^2+2y=48 | | 0.15x-4.25=0.5(x-5) | | 4z-6z+3=0 | | 4p^2+4x=35 | | 6m+2=1 | | 19=2(w+3)+5 | | r^4+4r^3+3r=0 | | y=0.833x-5 | | 3(2x+9)=38 | | 7-3x=-x+1 | | r^4+r^3+3r=0 | | (3x+4)2= |

Equations solver categories