17r+r^2=52

Simple and best practice solution for 17r+r^2=52 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 17r+r^2=52 equation:


Simplifying
17r + r2 = 52

Solving
17r + r2 = 52

Solving for variable 'r'.

Reorder the terms:
-52 + 17r + r2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 17r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 17r + 52 + r2 = 0 + 52

Reorder the terms:
-52 + 52 + 17r + r2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 17r + r2 = 0 + 52
17r + r2 = 0 + 52

Combine like terms: 0 + 52 = 52
17r + r2 = 52

The r term is 17r.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17r + 72.25 + r2 = 52 + 72.25

Reorder the terms:
72.25 + 17r + r2 = 52 + 72.25

Combine like terms: 52 + 72.25 = 124.25
72.25 + 17r + r2 = 124.25

Factor a perfect square on the left side:
(r + 8.5)(r + 8.5) = 124.25

Calculate the square root of the right side: 11.146748405

Break this problem into two subproblems by setting 
(r + 8.5) equal to 11.146748405 and -11.146748405.

Subproblem 1

r + 8.5 = 11.146748405 Simplifying r + 8.5 = 11.146748405 Reorder the terms: 8.5 + r = 11.146748405 Solving 8.5 + r = 11.146748405 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + r = 11.146748405 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + r = 11.146748405 + -8.5 r = 11.146748405 + -8.5 Combine like terms: 11.146748405 + -8.5 = 2.646748405 r = 2.646748405 Simplifying r = 2.646748405

Subproblem 2

r + 8.5 = -11.146748405 Simplifying r + 8.5 = -11.146748405 Reorder the terms: 8.5 + r = -11.146748405 Solving 8.5 + r = -11.146748405 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + r = -11.146748405 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + r = -11.146748405 + -8.5 r = -11.146748405 + -8.5 Combine like terms: -11.146748405 + -8.5 = -19.646748405 r = -19.646748405 Simplifying r = -19.646748405

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.646748405, -19.646748405}

See similar equations:

| 5(7q-3)= | | -9x+12=3(3x-4) | | 9n^2-5(5m^3+6n^2)= | | 5g+4(-5+3g)=7-g | | -1x-1=1-21 | | 4p+6=12 | | 6x+8.1=9.8 | | (x+4)*x=77 | | (3)(-5)= | | u^2+4=0 | | 7x+12=24 | | Q^2+7q-10=0 | | -g+12=14 | | a^2-18+80=0 | | -4n+1-6=-17 | | 3x-(4)=4 | | Y=7+5 | | 12s+(7-s)2= | | 12x+7=9x+15 | | -2x-8=4x-3(2x+12) | | 4s-12=-5s+21 | | 3(x)-4=4 | | 7-2x=1-5x+2x | | (8x^2+2y-6)+(2x^2+7y)= | | Y=6+5 | | -3(y+2)-6y= | | 8-3.5x=-20 | | 3(1)-y=4 | | 2n+1=3n-2 | | 7p-2=6p-2 | | 8+2m-5=9m+3-6m | | (x-2)(18x^2+83x+70)=0 |

Equations solver categories