y^2=-y+8

Simple and best practice solution for y^2=-y+8 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+8 equation: 


Simplifying
y2 = -1y + 8

Reorder the terms:
y2 = 8 + -1y

Solving
y2 = 8 + -1y

Solving for variable 'y'.

Reorder the terms:
-8 + y + y2 = 8 + -1y + -8 + y

Reorder the terms:
-8 + y + y2 = 8 + -8 + -1y + y

Combine like terms: 8 + -8 = 0
-8 + y + y2 = 0 + -1y + y
-8 + y + y2 = -1y + y

Combine like terms: -1y + y = 0
-8 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + y + y2 = 0 + 8
y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
y + y2 = 8

The y term is y.  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.
y + 0.25 + y2 = 8 + 0.25

Reorder the terms:
0.25 + y + y2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + y + y2 = 8.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
y + 0.5 = 2.872281323

Simplifying
y + 0.5 = 2.872281323

Reorder the terms:
0.5 + y = 2.872281323

Solving
0.5 + y = 2.872281323

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 = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.872281323 + -0.5
y = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
y = 2.372281323

Simplifying
y = 2.372281323


Subproblem 2
y + 0.5 = -2.872281323

Simplifying
y + 0.5 = -2.872281323

Reorder the terms:
0.5 + y = -2.872281323

Solving
0.5 + y = -2.872281323

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 = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.872281323 + -0.5
y = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
y = -3.372281323

Simplifying
y = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.372281323, -3.372281323}

See similar equations:

| C=2pi*10-12 | | x^2-2x=-11 | | 1.07x=87.34387283 | | 43+x+y=180 | | 4p+yx-x=-5q | | 1.07x=93.45794393 | | 5/12•3/2= | | 5/12•3/2 | | 2x-11=75 | | 0.5lnx=64 | | 9-81/2 | | (18+2x)(24+2x)=1360 | | 18+5y=2y | | 7x+21=11 | | x6=12/9 | | (x+18)(x+24)=1360 | | tan(5x)*(9x-1)=-5 | | y=(3+6k)x | | tan(5x)*(9t-1)=5 | | 6/11x5/10 | | (tan(5t))(9t-1)=-5 | | 8x+10x-6=7x+8 | | 250n+50n^2=25000 | | Logx^4=3 | | (3/2x-1)-(4/3x-1)=1 | | 2x+50=-2 | | (8x-1)+27=180 | | lnx-5[ln(x-7)+ln(x+7)]= | | 2b^2-7b+9-6= | | 3x^2+15x-8.1=0 | | a^2+5a+b=0 | | 9+3x=-2 |

Equations solver categories