(r-2)(r+12)=31

Simple and best practice solution for (r-2)(r+12)=31 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)(r+12)=31 equation:


Simplifying
(r + -2)(r + 12) = 31

Reorder the terms:
(-2 + r)(r + 12) = 31

Reorder the terms:
(-2 + r)(12 + r) = 31

Multiply (-2 + r) * (12 + r)
(-2(12 + r) + r(12 + r)) = 31
((12 * -2 + r * -2) + r(12 + r)) = 31
((-24 + -2r) + r(12 + r)) = 31
(-24 + -2r + (12 * r + r * r)) = 31
(-24 + -2r + (12r + r2)) = 31

Combine like terms: -2r + 12r = 10r
(-24 + 10r + r2) = 31

Solving
-24 + 10r + r2 = 31

Solving for variable 'r'.

Reorder the terms:
-24 + -31 + 10r + r2 = 31 + -31

Combine like terms: -24 + -31 = -55
-55 + 10r + r2 = 31 + -31

Combine like terms: 31 + -31 = 0
-55 + 10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 10r + 55 + r2 = 0 + 55

Reorder the terms:
-55 + 55 + 10r + r2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 10r + r2 = 0 + 55
10r + r2 = 0 + 55

Combine like terms: 0 + 55 = 55
10r + r2 = 55

The r term is 10r.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10r + 25 + r2 = 55 + 25

Reorder the terms:
25 + 10r + r2 = 55 + 25

Combine like terms: 55 + 25 = 80
25 + 10r + r2 = 80

Factor a perfect square on the left side:
(r + 5)(r + 5) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + 5) equal to 8.94427191 and -8.94427191.

Subproblem 1

r + 5 = 8.94427191 Simplifying r + 5 = 8.94427191 Reorder the terms: 5 + r = 8.94427191 Solving 5 + r = 8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + r = 8.94427191 + -5 r = 8.94427191 + -5 Combine like terms: 8.94427191 + -5 = 3.94427191 r = 3.94427191 Simplifying r = 3.94427191

Subproblem 2

r + 5 = -8.94427191 Simplifying r + 5 = -8.94427191 Reorder the terms: 5 + r = -8.94427191 Solving 5 + r = -8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + r = -8.94427191 + -5 r = -8.94427191 + -5 Combine like terms: -8.94427191 + -5 = -13.94427191 r = -13.94427191 Simplifying r = -13.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.94427191, -13.94427191}

See similar equations:

| .50+x=.60x+3 | | 6+5(y-9)=28 | | a^2+21a-10=0 | | 6x+42-4x-24= | | X+2.8=3.16 | | F(x)=-2x+7whatisf(-3) | | F(x)=-2x+7whatisf | | 1909=2*3.14*r*30+2*3.14*r^2 | | x/((0.30-x)(0.40-x))=4.26 | | 1909=2*3.14*r*30 | | x/(0.30-x)(0.40-x)=0 | | y=x^2+100 | | x-0.60x=6 | | 13=e^4x | | 2x^1/3-8=1 | | 46=47+-x | | g(14)=6/7(14)-4 | | x-x*(225-5-5x)+4-3x*5= | | 10(2x-1)=8(2x+1)+4 | | 9x+4x-2x=28+5 | | 7s+8s= | | -8x-11y-9x+6y= | | x-60x=56 | | 8x-(-13x)= | | x-20x=6 | | 4(3z+6)= | | 3(y-x)=2(y+x) | | 5(t-3)+7t=6(2t+3)-10 | | a-20=5 | | a+2.4=7 | | x-0.60x=56 | | (x+3)2=(x-2)2 |

Equations solver categories