(r-2)(r+10)=89

Simple and best practice solution for (r-2)(r+10)=89 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+10)=89 equation:


Simplifying
(r + -2)(r + 10) = 89

Reorder the terms:
(-2 + r)(r + 10) = 89

Reorder the terms:
(-2 + r)(10 + r) = 89

Multiply (-2 + r) * (10 + r)
(-2(10 + r) + r(10 + r)) = 89
((10 * -2 + r * -2) + r(10 + r)) = 89
((-20 + -2r) + r(10 + r)) = 89
(-20 + -2r + (10 * r + r * r)) = 89
(-20 + -2r + (10r + r2)) = 89

Combine like terms: -2r + 10r = 8r
(-20 + 8r + r2) = 89

Solving
-20 + 8r + r2 = 89

Solving for variable 'r'.

Reorder the terms:
-20 + -89 + 8r + r2 = 89 + -89

Combine like terms: -20 + -89 = -109
-109 + 8r + r2 = 89 + -89

Combine like terms: 89 + -89 = 0
-109 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '109' to each side of the equation.
-109 + 8r + 109 + r2 = 0 + 109

Reorder the terms:
-109 + 109 + 8r + r2 = 0 + 109

Combine like terms: -109 + 109 = 0
0 + 8r + r2 = 0 + 109
8r + r2 = 0 + 109

Combine like terms: 0 + 109 = 109
8r + r2 = 109

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 = 109 + 16

Reorder the terms:
16 + 8r + r2 = 109 + 16

Combine like terms: 109 + 16 = 125
16 + 8r + r2 = 125

Factor a perfect square on the left side:
(r + 4)(r + 4) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(r + 4) equal to 11.180339887 and -11.180339887.

Subproblem 1

r + 4 = 11.180339887 Simplifying r + 4 = 11.180339887 Reorder the terms: 4 + r = 11.180339887 Solving 4 + r = 11.180339887 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 = 11.180339887 + -4 Combine like terms: 4 + -4 = 0 0 + r = 11.180339887 + -4 r = 11.180339887 + -4 Combine like terms: 11.180339887 + -4 = 7.180339887 r = 7.180339887 Simplifying r = 7.180339887

Subproblem 2

r + 4 = -11.180339887 Simplifying r + 4 = -11.180339887 Reorder the terms: 4 + r = -11.180339887 Solving 4 + r = -11.180339887 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 = -11.180339887 + -4 Combine like terms: 4 + -4 = 0 0 + r = -11.180339887 + -4 r = -11.180339887 + -4 Combine like terms: -11.180339887 + -4 = -15.180339887 r = -15.180339887 Simplifying r = -15.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.180339887, -15.180339887}

See similar equations:

| 7(3x-2)+5x=6(2x-1)+24 | | 7n-9=2n+16 | | 6(n+3)=0 | | (r-2)(r+10)=9 | | 2x-13=x+41 | | -4(4n+2)=20 | | 8-4x=15-5x | | 3(3g+40)-9g-120=0 | | 2x-40=x-20 | | 0.8x-0.3(50+x)=0.2(50) | | (x-2y)dx+(2x+y)dy=0de | | y=2x^2+kx+4 | | Q=60-4Pforp | | 5t^2+4t=0 | | 5=-3n+4n | | 3x+8=12X | | 9=3x-8 | | S=7x^2y | | h+(2h-1000)=440 | | c/12=5 | | z+4=69 | | 24x^3-15x^2+8x-5= | | 4z-2-(1-z)=4 | | 3+9(x-4)=8-8(x-7) | | =(4x+3)(4x-3) | | (-5a^3b^3)(6ab^5)= | | 13-x=209 | | a-17=18 | | x+(2x+1000)=4400 | | 3(3k+5)-14k+8+5= | | 3x+17-x+17=-4 | | 10k+73=2(5k+34) |

Equations solver categories