r^2-12r+18=0

Simple and best practice solution for r^2-12r+18=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^2-12r+18=0 equation:


Simplifying
r2 + -12r + 18 = 0

Reorder the terms:
18 + -12r + r2 = 0

Solving
18 + -12r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -12r + -18 + r2 = 0 + -18

Reorder the terms:
18 + -18 + -12r + r2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -12r + r2 = 0 + -18
-12r + r2 = 0 + -18

Combine like terms: 0 + -18 = -18
-12r + r2 = -18

The r term is -12r.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12r + 36 + r2 = -18 + 36

Reorder the terms:
36 + -12r + r2 = -18 + 36

Combine like terms: -18 + 36 = 18
36 + -12r + r2 = 18

Factor a perfect square on the left side:
(r + -6)(r + -6) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(r + -6) equal to 4.242640687 and -4.242640687.

Subproblem 1

r + -6 = 4.242640687 Simplifying r + -6 = 4.242640687 Reorder the terms: -6 + r = 4.242640687 Solving -6 + r = 4.242640687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + r = 4.242640687 + 6 r = 4.242640687 + 6 Combine like terms: 4.242640687 + 6 = 10.242640687 r = 10.242640687 Simplifying r = 10.242640687

Subproblem 2

r + -6 = -4.242640687 Simplifying r + -6 = -4.242640687 Reorder the terms: -6 + r = -4.242640687 Solving -6 + r = -4.242640687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + r = -4.242640687 + 6 r = -4.242640687 + 6 Combine like terms: -4.242640687 + 6 = 1.757359313 r = 1.757359313 Simplifying r = 1.757359313

Solution

The solution to the problem is based on the solutions from the subproblems. r = {10.242640687, 1.757359313}

See similar equations:

| 18-7x=-3+2x | | 5(3x-7)-4(x+1)-20x= | | x^2-6x+6x=0 | | -2p-8p-9p-16p+(-18)=17 | | 3/10k+4=7 | | 4/5m+1=9 | | 64p^3-8q^3=0 | | 1575+160t+4t^2= | | 4+f=12 | | 2.45=3d+4d | | A=yv+yforv | | 39.21x+265=-31.68+42.03x | | 16=(x-3)(x+3) | | a(b+2c)= | | 31=8x-2+3x | | X^2+8x-140=0 | | 1.92=6z+2z | | -15x=150 | | y=-8x-13 | | 5+t=476 | | 7n+2=4k-10 | | -7m+6-5(m+1)=4m-2 | | -3b-9=-33 | | 88=17w+5w | | (x-1)(6x+5)=0 | | 39=t+2t | | 50+1m+9=93.23 | | -18+6n=60 | | 70000=15x+12y | | 5x-[2(x+1)+2]=7 | | a+9=4a | | x=3(5)-7 |

Equations solver categories