r^2-484=r

Simple and best practice solution for r^2-484=r 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^2-484=r equation:


Simplifying
r2 + -484 = r

Reorder the terms:
-484 + r2 = r

Solving
-484 + r2 = r

Solving for variable 'r'.

Reorder the terms:
-484 + -1r + r2 = r + -1r

Combine like terms: r + -1r = 0
-484 + -1r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '484' to each side of the equation.
-484 + -1r + 484 + r2 = 0 + 484

Reorder the terms:
-484 + 484 + -1r + r2 = 0 + 484

Combine like terms: -484 + 484 = 0
0 + -1r + r2 = 0 + 484
-1r + r2 = 0 + 484

Combine like terms: 0 + 484 = 484
-1r + r2 = 484

The r term is -1r.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1r + 0.25 + r2 = 484 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 484 + 0.25

Combine like terms: 484 + 0.25 = 484.25
0.25 + -1r + r2 = 484.25

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 484.25

Calculate the square root of the right side: 22.005681085

Break this problem into two subproblems by setting 
(r + -0.5) equal to 22.005681085 and -22.005681085.

Subproblem 1

r + -0.5 = 22.005681085 Simplifying r + -0.5 = 22.005681085 Reorder the terms: -0.5 + r = 22.005681085 Solving -0.5 + r = 22.005681085 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 22.005681085 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 22.005681085 + 0.5 r = 22.005681085 + 0.5 Combine like terms: 22.005681085 + 0.5 = 22.505681085 r = 22.505681085 Simplifying r = 22.505681085

Subproblem 2

r + -0.5 = -22.005681085 Simplifying r + -0.5 = -22.005681085 Reorder the terms: -0.5 + r = -22.005681085 Solving -0.5 + r = -22.005681085 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -22.005681085 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -22.005681085 + 0.5 r = -22.005681085 + 0.5 Combine like terms: -22.005681085 + 0.5 = -21.505681085 r = -21.505681085 Simplifying r = -21.505681085

Solution

The solution to the problem is based on the solutions from the subproblems. r = {22.505681085, -21.505681085}

See similar equations:

| (5p-4)-(3p+2)= | | 5x^2+6x=7 | | -5(x-3)=30 | | 1-16b=5b-41 | | 2x^2+5x=11 | | x+3=x-5 | | -2x+1-3(x-4)=4(3-x)+4 | | 2x+1-3(x-4)=4(3-x)+4 | | -2x+1-3(x-4)=(3-x)+4 | | 5-3x+2=7 | | 4x+3x+4=3 | | 9v^2-6v+1=0 | | 5x+2x+3x+4=0 | | -9(v-4)=6v-24 | | x=-2x | | 81-x+16=0 | | 2lnx-1=0 | | X+55.4=552.3 | | B(b+19)=0 | | (x+5)2=0 | | (4x-3)(x+5)= | | -10(n-2)=x | | -4r-5r=x | | x-1+(x+2)=-4(-5-x)-5 | | x=x^3+4x^2+x-6 | | x+25=11 | | 4y^2-12y+3=0 | | -2x^2+6y^2+12= | | (x-9)(x+9)=4(-x-15) | | x^2+y^2+8x-2y-8=0 | | 60-3x=15x+22 | | x^2+(-3)x+(-10)x=0 |

Equations solver categories