(r-4)(r+10)=31

Simple and best practice solution for (r-4)(r+10)=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-4)(r+10)=31 equation:


Simplifying
(r + -4)(r + 10) = 31

Reorder the terms:
(-4 + r)(r + 10) = 31

Reorder the terms:
(-4 + r)(10 + r) = 31

Multiply (-4 + r) * (10 + r)
(-4(10 + r) + r(10 + r)) = 31
((10 * -4 + r * -4) + r(10 + r)) = 31
((-40 + -4r) + r(10 + r)) = 31
(-40 + -4r + (10 * r + r * r)) = 31
(-40 + -4r + (10r + r2)) = 31

Combine like terms: -4r + 10r = 6r
(-40 + 6r + r2) = 31

Solving
-40 + 6r + r2 = 31

Solving for variable 'r'.

Reorder the terms:
-40 + -31 + 6r + r2 = 31 + -31

Combine like terms: -40 + -31 = -71
-71 + 6r + r2 = 31 + -31

Combine like terms: 31 + -31 = 0
-71 + 6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + 6r + 71 + r2 = 0 + 71

Reorder the terms:
-71 + 71 + 6r + r2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + 6r + r2 = 0 + 71
6r + r2 = 0 + 71

Combine like terms: 0 + 71 = 71
6r + r2 = 71

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = 71 + 9

Reorder the terms:
9 + 6r + r2 = 71 + 9

Combine like terms: 71 + 9 = 80
9 + 6r + r2 = 80

Factor a perfect square on the left side:
(r + 3)(r + 3) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + 3) equal to 8.94427191 and -8.94427191.

Subproblem 1

r + 3 = 8.94427191 Simplifying r + 3 = 8.94427191 Reorder the terms: 3 + r = 8.94427191 Solving 3 + r = 8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 8.94427191 + -3 Combine like terms: 3 + -3 = 0 0 + r = 8.94427191 + -3 r = 8.94427191 + -3 Combine like terms: 8.94427191 + -3 = 5.94427191 r = 5.94427191 Simplifying r = 5.94427191

Subproblem 2

r + 3 = -8.94427191 Simplifying r + 3 = -8.94427191 Reorder the terms: 3 + r = -8.94427191 Solving 3 + r = -8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -8.94427191 + -3 Combine like terms: 3 + -3 = 0 0 + r = -8.94427191 + -3 r = -8.94427191 + -3 Combine like terms: -8.94427191 + -3 = -11.94427191 r = -11.94427191 Simplifying r = -11.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.94427191, -11.94427191}

See similar equations:

| 4(2-2.5)=26 | | 9-(2x-10)=-12 | | 4=(1/2)^x | | 2x+3y+x-2y=equation | | x^2=269 | | 3.2/6.4=8/n | | 60t-50=15+-5 | | -10-4v=-74 | | -9/(5/9)-16/5= | | 50=-7x^2-28-3x | | a^2-7a-60= | | 5(2-3)+x=2x-3 | | 6x+21y=1 | | D=M(1+rt) | | 14x+14(9)=196 | | a^2-2a-36= | | b/313= | | 9=3/7u | | 3.82X-23000=6X | | -7/6w-26=-19 | | log(x+1)+log(x-4)=2 | | 3/7u=9 | | 4x-12+9x=5x-15-13 | | 3/4-2/7•21/8 | | 9log(2x+20)=18 | | 3=×/6-2 | | -7=-16w | | X+-9x+24=-8 | | (10x+7)(3x-2)=0 | | 32+5x=-18 | | X+4=10-4 | | 2.0-0.5X=12.5 |

Equations solver categories