(r-2)(r+6)=109

Simple and best practice solution for (r-2)(r+6)=109 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+6)=109 equation:


Simplifying
(r + -2)(r + 6) = 109

Reorder the terms:
(-2 + r)(r + 6) = 109

Reorder the terms:
(-2 + r)(6 + r) = 109

Multiply (-2 + r) * (6 + r)
(-2(6 + r) + r(6 + r)) = 109
((6 * -2 + r * -2) + r(6 + r)) = 109
((-12 + -2r) + r(6 + r)) = 109
(-12 + -2r + (6 * r + r * r)) = 109
(-12 + -2r + (6r + r2)) = 109

Combine like terms: -2r + 6r = 4r
(-12 + 4r + r2) = 109

Solving
-12 + 4r + r2 = 109

Solving for variable 'r'.

Reorder the terms:
-12 + -109 + 4r + r2 = 109 + -109

Combine like terms: -12 + -109 = -121
-121 + 4r + r2 = 109 + -109

Combine like terms: 109 + -109 = 0
-121 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + 4r + 121 + r2 = 0 + 121

Reorder the terms:
-121 + 121 + 4r + r2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + 4r + r2 = 0 + 121
4r + r2 = 0 + 121

Combine like terms: 0 + 121 = 121
4r + r2 = 121

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 = 121 + 4

Reorder the terms:
4 + 4r + r2 = 121 + 4

Combine like terms: 121 + 4 = 125
4 + 4r + r2 = 125

Factor a perfect square on the left side:
(r + 2)(r + 2) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(r + 2) equal to 11.180339887 and -11.180339887.

Subproblem 1

r + 2 = 11.180339887 Simplifying r + 2 = 11.180339887 Reorder the terms: 2 + r = 11.180339887 Solving 2 + r = 11.180339887 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 = 11.180339887 + -2 Combine like terms: 2 + -2 = 0 0 + r = 11.180339887 + -2 r = 11.180339887 + -2 Combine like terms: 11.180339887 + -2 = 9.180339887 r = 9.180339887 Simplifying r = 9.180339887

Subproblem 2

r + 2 = -11.180339887 Simplifying r + 2 = -11.180339887 Reorder the terms: 2 + r = -11.180339887 Solving 2 + r = -11.180339887 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 = -11.180339887 + -2 Combine like terms: 2 + -2 = 0 0 + r = -11.180339887 + -2 r = -11.180339887 + -2 Combine like terms: -11.180339887 + -2 = -13.180339887 r = -13.180339887 Simplifying r = -13.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. r = {9.180339887, -13.180339887}

See similar equations:

| y=100(200)+1000 | | y=100(100)+1000 | | 1/2+3/7 | | -(x+4)/3=-8 | | 5v^2+4=-21v | | x^5-y^5=0 | | 3/12(2x-12)=8/12(3x+9) | | a(a+7)=90 | | 8x^(17/19)-16=0 | | y=1/8(2) | | 3x+33-6=(5x+2)(5x+2) | | 4x^2-98x+258=0 | | x^3+20x^2+100x=0 | | 20x^2+100x=0 | | F(x)=x-9 | | x=(-4*y)/15 | | -13-1/4=7 | | F(x)=4-8x | | 1=3x-12 | | 6x(x-1)=20-13x | | 2(2)+4y=8 | | 2(1)+4y=8 | | 525.00+0.21*(x)=525 | | (3x)(3x)+3x=-8 | | 1.5x+6=3.5-x | | 6(0)+4y=24 | | 6(2)+4y=24 | | 6(1)+4y=24 | | 6x+4(1)=24 | | X-19-(6x-7)+4(-x-7)=54 | | 6x+4(0)=24 | | 12*12=144 |

Equations solver categories