r^2+4r-41=5

Simple and best practice solution for r^2+4r-41=5 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-41=5 equation: 


Simplifying
r2 + 4r + -41 = 5

Reorder the terms:
-41 + 4r + r2 = 5

Solving
-41 + 4r + r2 = 5

Solving for variable 'r'.

Reorder the terms:
-41 + -5 + 4r + r2 = 5 + -5

Combine like terms: -41 + -5 = -46
-46 + 4r + r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-46 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 4r + 46 + r2 = 0 + 46

Reorder the terms:
-46 + 46 + 4r + r2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 4r + r2 = 0 + 46
4r + r2 = 0 + 46

Combine like terms: 0 + 46 = 46
4r + r2 = 46

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 = 46 + 4

Reorder the terms:
4 + 4r + r2 = 46 + 4

Combine like terms: 46 + 4 = 50
4 + 4r + r2 = 50

Factor a perfect square on the left side:
(r + 2)(r + 2) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(r + 2) equal to 7.071067812 and -7.071067812.


Subproblem 1
r + 2 = 7.071067812

Simplifying
r + 2 = 7.071067812

Reorder the terms:
2 + r = 7.071067812

Solving
2 + r = 7.071067812

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 = 7.071067812 + -2

Combine like terms: 2 + -2 = 0
0 + r = 7.071067812 + -2
r = 7.071067812 + -2

Combine like terms: 7.071067812 + -2 = 5.071067812
r = 5.071067812

Simplifying
r = 5.071067812


Subproblem 2
r + 2 = -7.071067812

Simplifying
r + 2 = -7.071067812

Reorder the terms:
2 + r = -7.071067812

Solving
2 + r = -7.071067812

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 = -7.071067812 + -2

Combine like terms: 2 + -2 = 0
0 + r = -7.071067812 + -2
r = -7.071067812 + -2

Combine like terms: -7.071067812 + -2 = -9.071067812
r = -9.071067812

Simplifying
r = -9.071067812


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.071067812, -9.071067812}

See similar equations:

| -6(11x+3x)=-6(x+11) | | 0.5=g/3 | | 53/8= | | -2(q-9)=1/2(4-8q) | | 5(z+y)+6x= | | -15=3v+2(v-5) | | 13x-12x-23=22 | | 5/3/8= | | Logx4/25=-2 | | 5cosx+3=4 | | 192/4.5(3)= | | 5(-8+k)=40-4k | | -15=5(u+8)+6u | | 9=3x^2-18 | | (x+1)=10 | | x=7-3(3) | | 5(1x-8)=-35 | | 1x+589=69 | | 2x-1/3x^2 | | 5+91x=52+17x | | 10-3x=x-6 | | 3(-1x+2)=-15 | | -7(3-5x)=49 | | 5t^2+15t-90=0 | | -1/b=-2 | | X*1/3x | | Ln(x^2-4)^1/2 | | 7a-4-a=-3(1-3a)-(a+5) | | -2(7x-5)=-116 | | 6(n-7)=-90 | | -5(1-3x)+5x=3(6x-5) | | 3x^2+7xy+5y^2-6x-7y+15=0 |

Equations solver categories