r^2+21r+10=0

Simple and best practice solution for r^2+21r+10=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+21r+10=0 equation:


Simplifying
r2 + 21r + 10 = 0

Reorder the terms:
10 + 21r + r2 = 0

Solving
10 + 21r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 21r + -10 + r2 = 0 + -10

Reorder the terms:
10 + -10 + 21r + r2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 21r + r2 = 0 + -10
21r + r2 = 0 + -10

Combine like terms: 0 + -10 = -10
21r + r2 = -10

The r term is 21r.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21r + 110.25 + r2 = -10 + 110.25

Reorder the terms:
110.25 + 21r + r2 = -10 + 110.25

Combine like terms: -10 + 110.25 = 100.25
110.25 + 21r + r2 = 100.25

Factor a perfect square on the left side:
(r + 10.5)(r + 10.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(r + 10.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

r + 10.5 = 10.012492197 Simplifying r + 10.5 = 10.012492197 Reorder the terms: 10.5 + r = 10.012492197 Solving 10.5 + r = 10.012492197 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + r = 10.012492197 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + r = 10.012492197 + -10.5 r = 10.012492197 + -10.5 Combine like terms: 10.012492197 + -10.5 = -0.487507803 r = -0.487507803 Simplifying r = -0.487507803

Subproblem 2

r + 10.5 = -10.012492197 Simplifying r + 10.5 = -10.012492197 Reorder the terms: 10.5 + r = -10.012492197 Solving 10.5 + r = -10.012492197 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + r = -10.012492197 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + r = -10.012492197 + -10.5 r = -10.012492197 + -10.5 Combine like terms: -10.012492197 + -10.5 = -20.512492197 r = -20.512492197 Simplifying r = -20.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.487507803, -20.512492197}

See similar equations:

| 4(x+1)-3=-5 | | 6x-22=8x-12 | | 6x-22=2x-12 | | a=1/2(10x) | | x^3+4x^2-13x+2=0 | | -7(2x+5)=63 | | f(x)=13x^2-208x+624 | | 2x+35=37 | | 6+x+16=6x | | 10x16/10x16 | | 30=-16t+56t+6 | | 0.112x^2+0.2399x-0.2603=0 | | f(x)=x^2+12x-144 | | x+4=4x+2istrue | | f(x)=x^2+12x+144 | | 4x-1-5=180 | | 324^1/4 | | 5y+6-2y=51 | | 12-5n=120 | | (x+5y-2z)-(x-4y+3z)= | | -4/3h=7 | | 3(x+4)*-22=14x+28 | | 11-17=8y+9-7y | | x-5=(x+1)/2 | | 3(x+4)square-22=14x+28 | | x+5=(x+1)/2 | | 3(x+4)-22=14x+28 | | n/4=13 | | 6v+4+7=-7 | | 4x+y=23 | | 2-8.3+3.8= | | -9+5y=4x |

Equations solver categories