r^2+16r-85=-8

Simple and best practice solution for r^2+16r-85=-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+16r-85=-8 equation: 


Simplifying
r2 + 16r + -85 = -8

Reorder the terms:
-85 + 16r + r2 = -8

Solving
-85 + 16r + r2 = -8

Solving for variable 'r'.

Reorder the terms:
-85 + 8 + 16r + r2 = -8 + 8

Combine like terms: -85 + 8 = -77
-77 + 16r + r2 = -8 + 8

Combine like terms: -8 + 8 = 0
-77 + 16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + 16r + 77 + r2 = 0 + 77

Reorder the terms:
-77 + 77 + 16r + r2 = 0 + 77

Combine like terms: -77 + 77 = 0
0 + 16r + r2 = 0 + 77
16r + r2 = 0 + 77

Combine like terms: 0 + 77 = 77
16r + r2 = 77

The r term is 16r.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16r + 64 + r2 = 77 + 64

Reorder the terms:
64 + 16r + r2 = 77 + 64

Combine like terms: 77 + 64 = 141
64 + 16r + r2 = 141

Factor a perfect square on the left side:
(r + 8)(r + 8) = 141

Calculate the square root of the right side: 11.874342087

Break this problem into two subproblems by setting 
(r + 8) equal to 11.874342087 and -11.874342087.


Subproblem 1
r + 8 = 11.874342087

Simplifying
r + 8 = 11.874342087

Reorder the terms:
8 + r = 11.874342087

Solving
8 + r = 11.874342087

Solving for variable 'r'.

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

Add '-8' to each side of the equation.
8 + -8 + r = 11.874342087 + -8

Combine like terms: 8 + -8 = 0
0 + r = 11.874342087 + -8
r = 11.874342087 + -8

Combine like terms: 11.874342087 + -8 = 3.874342087
r = 3.874342087

Simplifying
r = 3.874342087


Subproblem 2
r + 8 = -11.874342087

Simplifying
r + 8 = -11.874342087

Reorder the terms:
8 + r = -11.874342087

Solving
8 + r = -11.874342087

Solving for variable 'r'.

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

Add '-8' to each side of the equation.
8 + -8 + r = -11.874342087 + -8

Combine like terms: 8 + -8 = 0
0 + r = -11.874342087 + -8
r = -11.874342087 + -8

Combine like terms: -11.874342087 + -8 = -19.874342087
r = -19.874342087

Simplifying
r = -19.874342087


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.874342087, -19.874342087}

See similar equations:

| (3*2)^2-7*3/(4-2)-(8-5) | | -31e=-18 | | -3.5=-2.1+y | | X+(x+6)=216 | | 2x-21=2x+7 | | 120=r+(20+r)+(20+r) | | 2X-6-(X-3)(2X-5)=145 | | X+4.9=3.7 | | B-(-47)=24 | | 7x+35=3x+3 | | 2x^3+8x^2+10x+6=0 | | P+(-127)=73 | | -10(n-2)=-110 | | 8*y-4= | | r^2+14r+45=-3 | | -1=y+99 | | 100+248=t-20+t | | -31=-5-5(1+5x) | | 7-10b=17 | | -17+a=-10 | | xy=3x+5x | | -7(n-9)=91 | | -23-(-23)=x | | 5n-n=24 | | 6-3y=12x | | -2x+10y-2z-16=0 | | -8(1+b)=-112 | | 4y+34=3y-1 | | 17y-4y-12y-17=18 | | -21=-14+y | | 18x^2-12x-6= | | 9a-3=96 |

Equations solver categories