r^2+r=8

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


Simplifying
r2 + r = 8

Reorder the terms:
r + r2 = 8

Solving
r + r2 = 8

Solving for variable 'r'.

Reorder the terms:
-8 + r + r2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + r + 8 + r2 = 0 + 8

Reorder the terms:
-8 + 8 + r + r2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + r + r2 = 0 + 8
r + r2 = 0 + 8

Combine like terms: 0 + 8 = 8
r + r2 = 8

The r term is r.  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.
r + 0.25 + r2 = 8 + 0.25

Reorder the terms:
0.25 + r + r2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + r + r2 = 8.25

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

Calculate the square root of the right side: 2.872281323

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


Subproblem 1
r + 0.5 = 2.872281323

Simplifying
r + 0.5 = 2.872281323

Reorder the terms:
0.5 + r = 2.872281323

Solving
0.5 + r = 2.872281323

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 2.872281323 + -0.5

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

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

Simplifying
r = 2.372281323


Subproblem 2
r + 0.5 = -2.872281323

Simplifying
r + 0.5 = -2.872281323

Reorder the terms:
0.5 + r = -2.872281323

Solving
0.5 + r = -2.872281323

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -2.872281323 + -0.5

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

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

Simplifying
r = -3.372281323


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

See similar equations:

| V-.9v+6=11 | | 125x^3-25x^2-5x+1=0 | | 10x+5-12X=17 | | 200x-125x+45000=43425-150 | | -3(2n-4)=4n-(5n-6) | | 4z=7z | | 5y+7-3y=5y-2 | | 6(8z-4)-[2(4z-3)+2]= | | (5x+18)=(6x-5) | | 56+z=98 | | 8=r^2+r | | 12+2y=10-12 | | a-4-8=-8 | | 5-1x=1x-5 | | 2(5+7v)-4=14v-6 | | x^2+4y^2=0 | | 8-2k=5k+4(4k+2) | | 8x+5=-4+2x+21 | | 4x=3(2)+8 | | 6x-10=-8+3y | | 5+6x=6+2x | | 6x-2x=4x+1 | | -9(x-3)-28=-1 | | 20x-10+8x-20=140-6x | | (x+20)=(3x+42) | | 27a^3b-75ab=0 | | A-b+c=12 | | 12-3x=3(4-1x) | | 2p-10p=6 | | 8(7m+4)=8(8+8m) | | r-4(2+r)=7-3r | | 49=-2x+6x+9 |

Equations solver categories