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:
r2 = 9 + 6r

Solving
r2 = 9 + 6r

Solving for variable 'r'.

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

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

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

Combine like terms: 6r + -6r = 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 = 7.242640687 r = 7.242640687 Simplifying r = 7.242640687

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 = -1.242640687 r = -1.242640687 Simplifying r = -1.242640687

Solution

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

See similar equations:

| 4(x+1)=6(x-1)-4 | | 5(3x-8)-6=5(x-2)+14 | | 2(4a-12)+3a=6a+2 | | r+8.3=-8.8 | | 2/3+3k/4=7/12 | | X*X=624 | | (x-2)/3-4=(x-3)/4 | | (4x+2n)-(8x+14n)= | | 7x/12-7=x/4+13 | | 4x=3x^2+1 | | 4=-8/5(-1)+b | | X*X+2x=624 | | 8-6(x+1)=9+x | | X+(X+6)+(X+6*2)=98 | | -5x+60=x | | 2.5-2(t-5)=19 | | X+(X+6)+2X=98 | | x(2x+7)=-3 | | x^2+(2x-2)=0 | | 4(x+3)=6x-2(-5+x) | | y-7=-6 | | y+9=4 | | 4-4(c-6)=c | | 4m+7=13 | | 2(2x+10)=2x-12 | | y+10=20 | | y+25=15 | | a+6=0 | | ln(x+3)+ln(x+2)=ln(2) | | 18=13+x | | 34+3n=5(-4+6n) | | (2/7)*(2/7)*(2/7)= |

Equations solver categories