r^2+8r-29=0

Simple and best practice solution for r^2+8r-29=0 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+8r-29=0 equation: 


Simplifying
r2 + 8r + -29 = 0

Reorder the terms:
-29 + 8r + r2 = 0

Solving
-29 + 8r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 8r + 29 + r2 = 0 + 29

Reorder the terms:
-29 + 29 + 8r + r2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 8r + r2 = 0 + 29
8r + r2 = 0 + 29

Combine like terms: 0 + 29 = 29
8r + r2 = 29

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 29 + 16

Reorder the terms:
16 + 8r + r2 = 29 + 16

Combine like terms: 29 + 16 = 45
16 + 8r + r2 = 45

Factor a perfect square on the left side:
(r + 4)(r + 4) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(r + 4) equal to 6.708203933 and -6.708203933.


Subproblem 1
r + 4 = 6.708203933

Simplifying
r + 4 = 6.708203933

Reorder the terms:
4 + r = 6.708203933

Solving
4 + r = 6.708203933

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = 6.708203933 + -4

Combine like terms: 4 + -4 = 0
0 + r = 6.708203933 + -4
r = 6.708203933 + -4

Combine like terms: 6.708203933 + -4 = 2.708203933
r = 2.708203933

Simplifying
r = 2.708203933


Subproblem 2
r + 4 = -6.708203933

Simplifying
r + 4 = -6.708203933

Reorder the terms:
4 + r = -6.708203933

Solving
4 + r = -6.708203933

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = -6.708203933 + -4

Combine like terms: 4 + -4 = 0
0 + r = -6.708203933 + -4
r = -6.708203933 + -4

Combine like terms: -6.708203933 + -4 = -10.708203933
r = -10.708203933

Simplifying
r = -10.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.708203933, -10.708203933}

See similar equations:

| 10+6X-3= | | 6.5+j=12 | | x+3=7x-35 | | c(2c+3)+c-3(7+4c)= | | 2c-15=c+4 | | 4x+x+4x+x+5=180 | | 7+3/7+1/4-5-1/14 | | 2(11m-10)+6=-6(-6m+2)-8 | | 6x+9x=14x | | 40k+80k=30k+90 | | 6t+1/6=t+4/12+t-2/12 | | -5(6n-4)+30n= | | 65x+2=933 | | 2d-5/2=5d+2/9 | | 3.9+1.5=x | | z-19=15 | | 40k+80k=30k+90k | | 3/2x+3x+x+2x | | r/2.1=5.6/4.9 | | -(z-9)+2(8z)+5= | | -250+25X=25X+250 | | 2.4+j=14.3 | | -12=11 | | 3x+42=4x+11 | | 15/2=17y/2+3/2(-7y+3) | | 0=12x^2+72x-84 | | t+1=-2p | | 3+3/7+4+1/4-5-1/14 | | 11=5m/-2 | | d^2=45 | | 7-x=3.5x | | 4m-21=-13 |

Equations solver categories