125+r^2+2r+1=180

Simple and best practice solution for 125+r^2+2r+1=180 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 125+r^2+2r+1=180 equation:


Simplifying
125 + r2 + 2r + 1 = 180

Reorder the terms:
125 + 1 + 2r + r2 = 180

Combine like terms: 125 + 1 = 126
126 + 2r + r2 = 180

Solving
126 + 2r + r2 = 180

Solving for variable 'r'.

Reorder the terms:
126 + -180 + 2r + r2 = 180 + -180

Combine like terms: 126 + -180 = -54
-54 + 2r + r2 = 180 + -180

Combine like terms: 180 + -180 = 0
-54 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 2r + 54 + r2 = 0 + 54

Reorder the terms:
-54 + 54 + 2r + r2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 2r + r2 = 0 + 54
2r + r2 = 0 + 54

Combine like terms: 0 + 54 = 54
2r + r2 = 54

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 54 + 1

Reorder the terms:
1 + 2r + r2 = 54 + 1

Combine like terms: 54 + 1 = 55
1 + 2r + r2 = 55

Factor a perfect square on the left side:
(r + 1)(r + 1) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(r + 1) equal to 7.416198487 and -7.416198487.

Subproblem 1

r + 1 = 7.416198487 Simplifying r + 1 = 7.416198487 Reorder the terms: 1 + r = 7.416198487 Solving 1 + r = 7.416198487 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + r = 7.416198487 + -1 r = 7.416198487 + -1 Combine like terms: 7.416198487 + -1 = 6.416198487 r = 6.416198487 Simplifying r = 6.416198487

Subproblem 2

r + 1 = -7.416198487 Simplifying r + 1 = -7.416198487 Reorder the terms: 1 + r = -7.416198487 Solving 1 + r = -7.416198487 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + r = -7.416198487 + -1 r = -7.416198487 + -1 Combine like terms: -7.416198487 + -1 = -8.416198487 r = -8.416198487 Simplifying r = -8.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.416198487, -8.416198487}

See similar equations:

| 35-2x=7x+18 | | 1.26x+2.16=7.71 | | (x*x)-3x-6=0 | | 5+4x=-43 | | x^2-x+13=0 | | 5(2x-1)=3(5x-4) | | -3(x+2)=-3x+6 | | 4x-10=-10 | | 20p^2t^2-10pt^5= | | x+5/5+x-1/2=x-1/3 | | -2x^2-x-11=0 | | .5x+.25=.5 | | 12x^2-4xy-9x+3y= | | 10-4c= | | k^2-18k+81=0 | | 2(x-7)= | | 36=51-3x | | -10-2x=-14 | | 52/64= | | 7+2x=-1 | | 12-8x=182-43x | | 3(x-6)=31-4x | | (.25)m-6=2m+18 | | x^4-8x^2-20=y | | 16p+20q+p-4q-6p=0 | | 3x^2+18x=81 | | -2(3x-4)=4x-12 | | 5(2+3y)=(2y+5)3 | | 4x-7=53-8x | | -16t^2+1499=45 | | -16t^2+1399=0 | | 10m+6n-2m+11n=0 |

Equations solver categories