y^2-y=2015

Simple and best practice solution for y^2-y=2015 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-y=2015 equation: 


Simplifying
y2 + -1y = 2015

Reorder the terms:
-1y + y2 = 2015

Solving
-1y + y2 = 2015

Solving for variable 'y'.

Reorder the terms:
-2015 + -1y + y2 = 2015 + -2015

Combine like terms: 2015 + -2015 = 0
-2015 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2015' to each side of the equation.
-2015 + -1y + 2015 + y2 = 0 + 2015

Reorder the terms:
-2015 + 2015 + -1y + y2 = 0 + 2015

Combine like terms: -2015 + 2015 = 0
0 + -1y + y2 = 0 + 2015
-1y + y2 = 0 + 2015

Combine like terms: 0 + 2015 = 2015
-1y + y2 = 2015

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 2015 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 2015 + 0.25

Combine like terms: 2015 + 0.25 = 2015.25
0.25 + -1y + y2 = 2015.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 2015.25

Calculate the square root of the right side: 44.891535951

Break this problem into two subproblems by setting 
(y + -0.5) equal to 44.891535951 and -44.891535951.


Subproblem 1
y + -0.5 = 44.891535951

Simplifying
y + -0.5 = 44.891535951

Reorder the terms:
-0.5 + y = 44.891535951

Solving
-0.5 + y = 44.891535951

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 44.891535951 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 44.891535951 + 0.5
y = 44.891535951 + 0.5

Combine like terms: 44.891535951 + 0.5 = 45.391535951
y = 45.391535951

Simplifying
y = 45.391535951


Subproblem 2
y + -0.5 = -44.891535951

Simplifying
y + -0.5 = -44.891535951

Reorder the terms:
-0.5 + y = -44.891535951

Solving
-0.5 + y = -44.891535951

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -44.891535951 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -44.891535951 + 0.5
y = -44.891535951 + 0.5

Combine like terms: -44.891535951 + 0.5 = -44.391535951
y = -44.391535951

Simplifying
y = -44.391535951


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {45.391535951, -44.391535951}

See similar equations:

| x+95=5x | | 2y-5+8=4 | | -9-(-14)+5(16-3)= | | 12=4+n | | 2y-5+4=8 | | 5*345355a-66/3 | | 5(3)+y=5 | | 5(2)+y=5 | | f(x)=x^2+8x | | 5(1)+y=5 | | 5(0)+y=5 | | (2)+y=5 | | 3x-37.5=94.5 | | (1)+y=5 | | (0)+y=5 | | Y=-4x^2-8x-13 | | 6(3)+y=-4 | | 165=6(2x) | | 6(2)+y=-4 | | 6(1)+y=-4 | | 6(0)+y=-4 | | Msquared=81 | | 12n+2=60 | | 0.5x+26.1=50.6 | | 3(1)+y=1 | | 0=2w+2.7-13.25 | | 3(2)+y=1 | | 1/4(3x-12)=-1/4x-3 | | 3(0)+y=1 | | 151=x+83 | | -2(2t+8)=-20 | | 4x+y=70 |

Equations solver categories