r^2+2r-9=-2

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


Simplifying
r2 + 2r + -9 = -2

Reorder the terms:
-9 + 2r + r2 = -2

Solving
-9 + 2r + r2 = -2

Solving for variable 'r'.

Reorder the terms:
-9 + 2 + 2r + r2 = -2 + 2

Combine like terms: -9 + 2 = -7
-7 + 2r + r2 = -2 + 2

Combine like terms: -2 + 2 = 0
-7 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + 2r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2r + r2 = 0 + 7
2r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
2r + r2 = 7

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 7 + 1

Reorder the terms:
1 + 2r + r2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + 2r + r2 = 8

Factor a perfect square on the left side:
(r + 1)(r + 1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(r + 1) equal to 2.828427125 and -2.828427125.


Subproblem 1
r + 1 = 2.828427125

Simplifying
r + 1 = 2.828427125

Reorder the terms:
1 + r = 2.828427125

Solving
1 + r = 2.828427125

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = 2.828427125 + -1

Combine like terms: 1 + -1 = 0
0 + r = 2.828427125 + -1
r = 2.828427125 + -1

Combine like terms: 2.828427125 + -1 = 1.828427125
r = 1.828427125

Simplifying
r = 1.828427125


Subproblem 2
r + 1 = -2.828427125

Simplifying
r + 1 = -2.828427125

Reorder the terms:
1 + r = -2.828427125

Solving
1 + r = -2.828427125

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = -2.828427125 + -1

Combine like terms: 1 + -1 = 0
0 + r = -2.828427125 + -1
r = -2.828427125 + -1

Combine like terms: -2.828427125 + -1 = -3.828427125
r = -3.828427125

Simplifying
r = -3.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.828427125, -3.828427125}

See similar equations:

| 2-5(x+2)=2x+3 | | 6(x-7)-7(x-6)=x+6-(x-6) | | 3+4y=27 | | 0.3x+1.4=0.8x-0.6 | | 4(x-2)+13=3(x+4) | | y+2y+3y=20 | | 5(6z-1)-5(Z+9)=23 | | 3x^2-8x-3= | | 5(6z-1)-5-5(Z+9)=23 | | 6x+6=3x+48 | | 4y-3=11y+18 | | 8x-(5x-9)=30 | | x^3-4x^2+4x-2=0 | | X^2-15x-14=0 | | 3x^4+7x^2=76 | | 6x+2-2x=4x+1 | | 329-42y+6y=5 | | 4x-(-3)=15 | | 5(4z-1)-2(2+9)=16(2+1) | | (E^9)=0 | | 5x+4=8x-6 | | 3x+38=12x-43 | | =(2x+5)(2x+5) | | 14=30-p | | 3x+3=6x-6 | | -3x+3(-2x+2)=42 | | 2s^2+5s+8=0 | | -60=-3(4+4v) | | 16n^2-64n+64=0 | | 2x-2x=2+2x+2 | | 49=-3-4(4v+3) | | 57=4(-4x+2)-1 |

Equations solver categories