r^2+18r+31=0

Simple and best practice solution for r^2+18r+31=0 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+18r+31=0 equation:


Simplifying
r2 + 18r + 31 = 0

Reorder the terms:
31 + 18r + r2 = 0

Solving
31 + 18r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 18r + -31 + r2 = 0 + -31

Reorder the terms:
31 + -31 + 18r + r2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 18r + r2 = 0 + -31
18r + r2 = 0 + -31

Combine like terms: 0 + -31 = -31
18r + r2 = -31

The r term is 18r.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18r + 81 + r2 = -31 + 81

Reorder the terms:
81 + 18r + r2 = -31 + 81

Combine like terms: -31 + 81 = 50
81 + 18r + r2 = 50

Factor a perfect square on the left side:
(r + 9)(r + 9) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(r + 9) equal to 7.071067812 and -7.071067812.

Subproblem 1

r + 9 = 7.071067812 Simplifying r + 9 = 7.071067812 Reorder the terms: 9 + r = 7.071067812 Solving 9 + r = 7.071067812 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = 7.071067812 + -9 Combine like terms: 9 + -9 = 0 0 + r = 7.071067812 + -9 r = 7.071067812 + -9 Combine like terms: 7.071067812 + -9 = -1.928932188 r = -1.928932188 Simplifying r = -1.928932188

Subproblem 2

r + 9 = -7.071067812 Simplifying r + 9 = -7.071067812 Reorder the terms: 9 + r = -7.071067812 Solving 9 + r = -7.071067812 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = -7.071067812 + -9 Combine like terms: 9 + -9 = 0 0 + r = -7.071067812 + -9 r = -7.071067812 + -9 Combine like terms: -7.071067812 + -9 = -16.071067812 r = -16.071067812 Simplifying r = -16.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-1.928932188, -16.071067812}

See similar equations:

| 11y-16y=10 | | 3x+2(2x-1)=5(x+4) | | 8p+12p=80 | | 4y^2+64y-116=0 | | -4x^2+550x+8500=0 | | 4(6x-5)-9=24x-29 | | 6m+18=42 | | z^2-4z-23=0 | | 4x+8=2x-22 | | 7z=1055 | | 3r=-150 | | 1+2m=8 | | 7t=-126 | | s^2+28s=15 | | 2x+160450=311950 | | 2x+160450=411 | | 14(z+2)-3(z-2)=5(z-1)+5(z-2) | | 2p^2+28p=-26 | | x+26=5x+34 | | 49x^2+9x-468=0 | | 6.33*x=0.60 | | X+(x+160450)=311950 | | x-18y=-40 | | X+x+160450=311950 | | 18=-3(1-x)+5(x+1) | | (-1)-3y=9 | | 7m=3m-28 | | -1-3y=9 | | 30=7(2.5x)+7(x) | | factorg^2+3g-40=0 | | 6n^2+10n-3=0 | | 2(2-3x)=2(3x+1) |

Equations solver categories