3r+r^2=9

Simple and best practice solution for 3r+r^2=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 3r+r^2=9 equation:


Simplifying
3r + r2 = 9

Solving
3r + r2 = 9

Solving for variable 'r'.

Reorder the terms:
-9 + 3r + r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 3r + 9 + r2 = 0 + 9

Reorder the terms:
-9 + 9 + 3r + r2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3r + r2 = 0 + 9
3r + r2 = 0 + 9

Combine like terms: 0 + 9 = 9
3r + r2 = 9

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 9 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + 3r + r2 = 11.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(r + 1.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

r + 1.5 = 3.354101966 Simplifying r + 1.5 = 3.354101966 Reorder the terms: 1.5 + r = 3.354101966 Solving 1.5 + r = 3.354101966 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 3.354101966 + -1.5 r = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 r = 1.854101966 Simplifying r = 1.854101966

Subproblem 2

r + 1.5 = -3.354101966 Simplifying r + 1.5 = -3.354101966 Reorder the terms: 1.5 + r = -3.354101966 Solving 1.5 + r = -3.354101966 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -3.354101966 + -1.5 r = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 r = -4.854101966 Simplifying r = -4.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.854101966, -4.854101966}

See similar equations:

| 5u^2+12u-9= | | 2v^2+9tv+4t^2= | | R(r+3)=9 | | 9^2x=1/3 | | X(x+4)=1152 | | 6X*-16X-11=0 | | 2(x+8)=7(x-2) | | m^2-3m-1=0 | | 20-(P/2) | | 2(x+3)=2(x+9) | | 12x(5-2y)=40 | | 4x-9y=-48 | | 8y-24/4 | | qx=mx+p | | 6c^2-24=0 | | 2(15+y)=39+y | | 510-12q-0.012q^2=0 | | m^2+9mn+14n^2= | | 2y=12y-19 | | 6ax+9a= | | 9a+5=4a+5 | | 24x=11x | | 2y=12-19 | | 590-12q-0.012q^2=0 | | 2x^2-5x-56=0 | | Sec^2x+tan=3 | | (1-2)x-x/7=5 | | 8x+15=8x-15 | | 26/x-1=0 | | 5w-2=l | | 4x^2+x-120=y | | 6v^2-12v=p |

Equations solver categories