r^2+4r=30

Simple and best practice solution for r^2+4r=30 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+4r=30 equation: 


Simplifying
r2 + 4r = 30

Reorder the terms:
4r + r2 = 30

Solving
4r + r2 = 30

Solving for variable 'r'.

Reorder the terms:
-30 + 4r + r2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 4r + 30 + r2 = 0 + 30

Reorder the terms:
-30 + 30 + 4r + r2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 4r + r2 = 0 + 30
4r + r2 = 0 + 30

Combine like terms: 0 + 30 = 30
4r + r2 = 30

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 30 + 4

Reorder the terms:
4 + 4r + r2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + 4r + r2 = 34

Factor a perfect square on the left side:
(r + 2)(r + 2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(r + 2) equal to 5.830951895 and -5.830951895.


Subproblem 1
r + 2 = 5.830951895

Simplifying
r + 2 = 5.830951895

Reorder the terms:
2 + r = 5.830951895

Solving
2 + r = 5.830951895

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = 5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + r = 5.830951895 + -2
r = 5.830951895 + -2

Combine like terms: 5.830951895 + -2 = 3.830951895
r = 3.830951895

Simplifying
r = 3.830951895


Subproblem 2
r + 2 = -5.830951895

Simplifying
r + 2 = -5.830951895

Reorder the terms:
2 + r = -5.830951895

Solving
2 + r = -5.830951895

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = -5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + r = -5.830951895 + -2
r = -5.830951895 + -2

Combine like terms: -5.830951895 + -2 = -7.830951895
r = -7.830951895

Simplifying
r = -7.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.830951895, -7.830951895}

See similar equations:

| 3y=-3-4 | | 10b-4=6 | | 6x+7=6(x+5) | | 9x+35=53 | | 4x^2+-6x-9=0 | | 5.4+1.2n=2.40 | | 3.4(2.5x+2.8)=9 | | x^2=-7-7 | | 124+37=180 | | 4.9+1.8n=1.2 | | g^2+17g+c=0 | | 18(x-1)=6(3x+2)-30 | | 2x+y=-72 | | 32y+5y= | | 3x-10+30=180 | | 2/t+4/3t=4/t+2 | | 16t^2+25t-7=0 | | 6b+7b-10= | | 120+(22*x)=98+(6*x) | | 1/8t*24 | | 9y-4x=68 | | .7x+.8=.9x-.6 | | (2x^2y)^3/4y | | 7x-5y=-133 | | 8(x-11)=-2(x-41) | | 1/8*24 | | 4h-12=16 | | 7/3*24 | | 98*x=120*(98*2) | | 5=q/-2-5 | | (4r^3+4r)-(3r^3-2r)=0 | | (3x+5u)(7x-5u-4)=0 |

Equations solver categories