r^2+6r=9

Simple and best practice solution for r^2+6r=9 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+6r=9 equation:


Simplifying
r2 + 6r = 9

Reorder the terms:
6r + r2 = 9

Solving
6r + r2 = 9

Solving for variable 'r'.

Reorder the terms:
-9 + 6r + r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 6r + 9 + r2 = 0 + 9

Reorder the terms:
-9 + 9 + 6r + r2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 6r + r2 = 0 + 9
6r + r2 = 0 + 9

Combine like terms: 0 + 9 = 9
6r + r2 = 9

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = 9 + 9

Reorder the terms:
9 + 6r + r2 = 9 + 9

Combine like terms: 9 + 9 = 18
9 + 6r + r2 = 18

Factor a perfect square on the left side:
(r + 3)(r + 3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(r + 3) equal to 4.242640687 and -4.242640687.

Subproblem 1

r + 3 = 4.242640687 Simplifying r + 3 = 4.242640687 Reorder the terms: 3 + r = 4.242640687 Solving 3 + r = 4.242640687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + r = 4.242640687 + -3 r = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 r = 1.242640687 Simplifying r = 1.242640687

Subproblem 2

r + 3 = -4.242640687 Simplifying r + 3 = -4.242640687 Reorder the terms: 3 + r = -4.242640687 Solving 3 + r = -4.242640687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + r = -4.242640687 + -3 r = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 r = -7.242640687 Simplifying r = -7.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.242640687, -7.242640687}

See similar equations:

| 17x+13=79+10x-3 | | 18x-(17x-9)=-149 | | 100y= | | 9=2c+3 | | 9=3c+3 | | 9X-21=35minusX | | 10x+10=53+6x-3 | | g^2-24g+80=0 | | 5x=x+28 | | ln(6x+11)=ln(5x+6) | | 4x-0.8+3x-0.05= | | 2x+4x-12=0 | | 16=-(2+n) | | 2l+2w=102 | | 4b-11=17 | | 0.6x+14.2=x-2.72 | | (X+3)(x-3)(x)=440 | | 3+8lnx=2 | | 4(4x-2.1)=7x-8.4 | | 24x-6-13x+3=23x-5-12x+11 | | 3v-5=40 | | logx+2logx=12 | | 7(x-2.1)=4.9 | | 7p^3-5=51 | | 5-3x=y | | 60=-5(x-6) | | 43425-125x+200x=45000-150x | | 3+4X=9Xplus | | 4(8+c)-8(9-c)= | | 10y^2+200y-400=0 | | (9b-b)-2= | | 17x+13=79+6x-3 |

Equations solver categories