r^2-16r+64=54

Simple and best practice solution for r^2-16r+64=54 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+64=54 equation:


Simplifying
r2 + -16r + 64 = 54

Reorder the terms:
64 + -16r + r2 = 54

Solving
64 + -16r + r2 = 54

Solving for variable 'r'.

Reorder the terms:
64 + -54 + -16r + r2 = 54 + -54

Combine like terms: 64 + -54 = 10
10 + -16r + r2 = 54 + -54

Combine like terms: 54 + -54 = 0
10 + -16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -16r + -10 + r2 = 0 + -10

Reorder the terms:
10 + -10 + -16r + r2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -16r + r2 = 0 + -10
-16r + r2 = 0 + -10

Combine like terms: 0 + -10 = -10
-16r + r2 = -10

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 = -10 + 64

Reorder the terms:
64 + -16r + r2 = -10 + 64

Combine like terms: -10 + 64 = 54
64 + -16r + r2 = 54

Factor a perfect square on the left side:
(r + -8)(r + -8) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(r + -8) equal to 7.348469228 and -7.348469228.

Subproblem 1

r + -8 = 7.348469228 Simplifying r + -8 = 7.348469228 Reorder the terms: -8 + r = 7.348469228 Solving -8 + r = 7.348469228 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 = 7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + r = 7.348469228 + 8 r = 7.348469228 + 8 Combine like terms: 7.348469228 + 8 = 15.348469228 r = 15.348469228 Simplifying r = 15.348469228

Subproblem 2

r + -8 = -7.348469228 Simplifying r + -8 = -7.348469228 Reorder the terms: -8 + r = -7.348469228 Solving -8 + r = -7.348469228 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 = -7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + r = -7.348469228 + 8 r = -7.348469228 + 8 Combine like terms: -7.348469228 + 8 = 0.651530772 r = 0.651530772 Simplifying r = 0.651530772

Solution

The solution to the problem is based on the solutions from the subproblems. r = {15.348469228, 0.651530772}

See similar equations:

| 3(3w-4)=-30 | | (3y+1)+(2y+2)=132 | | 4x-5+3x+10=90 | | 8d+4d+5d-4=3d | | 3q+15q-1=17q-20 | | 6a-16+2= | | f(x)=(2x-27)(x^2+54) | | 7(2p+2)-8=6p+29 | | -18-4s=-4+3s | | -18-4s=-4+4s | | x^2+5x+2=3x+9 | | (2v+4)=170 | | -2.9u+5.76-12.26=-3.9u-19.2 | | m/5=-23 | | 2a-20=3a-10 | | -3w+19=-5(w-3) | | 89x+17+6x+5x-19= | | 8x=3x+2 | | 31(u+386)=496 | | 3x-y=33 | | X-27=-88 | | f(x)=(2x-21)(x^2+36) | | D+102=-2d-6 | | -13-17n=6-16n | | x/4=1=19 | | 3x-90=53-8x | | -8z+5z-17=-47 | | 2x+-3=-2x-3 | | 4+-9=3p | | 5f=-70 | | 2y^2+1y-1=0 | | 5/3xi/3 |

Equations solver categories