r^2+16r=-11

Simple and best practice solution for r^2+16r=-11 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+16r=-11 equation:


Simplifying
r2 + 16r = -11

Reorder the terms:
16r + r2 = -11

Solving
16r + r2 = -11

Solving for variable 'r'.

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

Combine like terms: -11 + 11 = 0
11 + 16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 16r + -11 + r2 = 0 + -11

Reorder the terms:
11 + -11 + 16r + r2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 16r + r2 = 0 + -11
16r + r2 = 0 + -11

Combine like terms: 0 + -11 = -11
16r + r2 = -11

The r term is 16r.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16r + 64 + r2 = -11 + 64

Reorder the terms:
64 + 16r + r2 = -11 + 64

Combine like terms: -11 + 64 = 53
64 + 16r + r2 = 53

Factor a perfect square on the left side:
(r + 8)(r + 8) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(r + 8) equal to 7.280109889 and -7.280109889.

Subproblem 1

r + 8 = 7.280109889 Simplifying r + 8 = 7.280109889 Reorder the terms: 8 + r = 7.280109889 Solving 8 + r = 7.280109889 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 7.280109889 + -8 Combine like terms: 8 + -8 = 0 0 + r = 7.280109889 + -8 r = 7.280109889 + -8 Combine like terms: 7.280109889 + -8 = -0.719890111 r = -0.719890111 Simplifying r = -0.719890111

Subproblem 2

r + 8 = -7.280109889 Simplifying r + 8 = -7.280109889 Reorder the terms: 8 + r = -7.280109889 Solving 8 + r = -7.280109889 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -7.280109889 + -8 Combine like terms: 8 + -8 = 0 0 + r = -7.280109889 + -8 r = -7.280109889 + -8 Combine like terms: -7.280109889 + -8 = -15.280109889 r = -15.280109889 Simplifying r = -15.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.719890111, -15.280109889}

See similar equations:

| y=-2*x+b | | -2y^2-16y+2=0 | | -44=2(2-8x) | | f(x)=x^3+4x^3-9x-36 | | 0.12(y-1)+0.18y=0.16y-0.01(40) | | 8(j+60)=600 | | 7sinx-2cosx=-4 | | w^2-26w=-31 | | 70+20n=250 | | 210+0.25x=395 | | -33-(-89)=m | | -(5x+3)=-33 | | a=-63+(-87) | | 2t^2-32t+94=0 | | x^(1/3)-x^2 | | 8x+4y=43 | | log(x)13=3 | | 2=22+2 | | 3x(1/8) | | 7x-5(7-x)=13 | | y=27-(-28) | | x^1/3-x^2=0 | | 48=4/3x | | 3n+4=2n-6 | | m^2+22m-7=0 | | 14+(-72)=z | | 4(8c-1)-8=30c+4 | | -62=-8(3n+4)-6n | | 12b^2-13b+3=0 | | 4(7b+8)=2(13b+28) | | Y=-.005x^2+.05x | | 4(8c-1)-12=30c+4 |

Equations solver categories