(r-2)(r+10)=-9

Simple and best practice solution for (r-2)(r+10)=-9 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)=-9 equation:


Simplifying
(r + -2)(r + 10) = -9

Reorder the terms:
(-2 + r)(r + 10) = -9

Reorder the terms:
(-2 + r)(10 + r) = -9

Multiply (-2 + r) * (10 + r)
(-2(10 + r) + r(10 + r)) = -9
((10 * -2 + r * -2) + r(10 + r)) = -9
((-20 + -2r) + r(10 + r)) = -9
(-20 + -2r + (10 * r + r * r)) = -9
(-20 + -2r + (10r + r2)) = -9

Combine like terms: -2r + 10r = 8r
(-20 + 8r + r2) = -9

Solving
-20 + 8r + r2 = -9

Solving for variable 'r'.

Reorder the terms:
-20 + 9 + 8r + r2 = -9 + 9

Combine like terms: -20 + 9 = -11
-11 + 8r + r2 = -9 + 9

Combine like terms: -9 + 9 = 0
-11 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 8r + 11 + r2 = 0 + 11

Reorder the terms:
-11 + 11 + 8r + r2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 8r + r2 = 0 + 11
8r + r2 = 0 + 11

Combine like terms: 0 + 11 = 11
8r + r2 = 11

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 = 11 + 16

Reorder the terms:
16 + 8r + r2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + 8r + r2 = 27

Factor a perfect square on the left side:
(r + 4)(r + 4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(r + 4) equal to 5.196152423 and -5.196152423.

Subproblem 1

r + 4 = 5.196152423 Simplifying r + 4 = 5.196152423 Reorder the terms: 4 + r = 5.196152423 Solving 4 + r = 5.196152423 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 = 5.196152423 + -4 Combine like terms: 4 + -4 = 0 0 + r = 5.196152423 + -4 r = 5.196152423 + -4 Combine like terms: 5.196152423 + -4 = 1.196152423 r = 1.196152423 Simplifying r = 1.196152423

Subproblem 2

r + 4 = -5.196152423 Simplifying r + 4 = -5.196152423 Reorder the terms: 4 + r = -5.196152423 Solving 4 + r = -5.196152423 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 = -5.196152423 + -4 Combine like terms: 4 + -4 = 0 0 + r = -5.196152423 + -4 r = -5.196152423 + -4 Combine like terms: -5.196152423 + -4 = -9.196152423 r = -9.196152423 Simplifying r = -9.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.196152423, -9.196152423}

See similar equations:

| X-5/14=4/7 | | 1-(2)/(5)y=4x-3 | | (4x-28)+(9x-17)+30=180 | | (7+7d)+(-5+9m)= | | 2.2x=12.76 | | 6.3k-1.4+3.5=52.5 | | -(2k+4)-4(k+4)=4k-8k | | 14x^2-46x+1=0 | | f(-1)=8x^5+2x | | 2s-1s= | | 3(1+6p)=-5p+3 | | F(x)=4x^2+2x+6 | | (3z-2)/-56 | | w^4=144 | | 3.4-4x= | | x-0.02x=510 | | 9(2h+3)-4(4h-6)= | | x+y+115=180 | | 32k-4=5k-32 | | (7+6x)+(-5+7d)= | | 3x-8y=34 | | 21*2x+8=27x | | =15x^2-4 | | 13x+11=20x-38 | | -8p+8p+2=p-4 | | (5x-1)/33 | | -(1+4x)=-5x-8 | | 5-2(4p-3)+25= | | 4e^3x=256 | | 8+3n=35 | | 5x-1/33 | | (6c+7)+(8y-5)= |

Equations solver categories