r^2-10r=-1

Simple and best practice solution for r^2-10r=-1 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^2-10r=-1 equation:


Simplifying
r2 + -10r = -1

Reorder the terms:
-10r + r2 = -1

Solving
-10r + r2 = -1

Solving for variable 'r'.

Reorder the terms:
1 + -10r + r2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -10r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + -10r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10r + r2 = 0 + -1
-10r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10r + r2 = -1

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = -1 + 25

Reorder the terms:
25 + -10r + r2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + -10r + r2 = 24

Factor a perfect square on the left side:
(r + -5)(r + -5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(r + -5) equal to 4.898979486 and -4.898979486.

Subproblem 1

r + -5 = 4.898979486 Simplifying r + -5 = 4.898979486 Reorder the terms: -5 + r = 4.898979486 Solving -5 + r = 4.898979486 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + r = 4.898979486 + 5 r = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 r = 9.898979486 Simplifying r = 9.898979486

Subproblem 2

r + -5 = -4.898979486 Simplifying r + -5 = -4.898979486 Reorder the terms: -5 + r = -4.898979486 Solving -5 + r = -4.898979486 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + r = -4.898979486 + 5 r = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 r = 0.101020514 Simplifying r = 0.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. r = {9.898979486, 0.101020514}

See similar equations:

| 9u-3v=7 | | 4x(2+x)=7 | | 8y+4(3+y)=3(y-7)+10y | | 467.50=210+1.03x | | 8x-3(1+7x)=-107 | | Y+7=1 | | 4(2b-3)-5b=6b+18 | | -3(2d+2)+9d=6 | | 2x-11=7x-19 | | 3x^2+7=4x^2-9 | | -4(1-8n)-3=185 | | -4 = d+7-3 | | 4m^2-8=304 | | 3.7x+8.1-5.3x=-7.2+2x | | 4x-2(x-5)=-6+4x+8 | | G+16=6 | | 2x-2=5x-50 | | 3x^2+7=4x^2-2 | | 1y+2x=7 | | 7m+7-5m+4= | | 2x-1+28=3x+22 | | 96000+420x/67000+300x=151500/106875 | | 16x^6-1=0 | | (x+3)+9=12 | | 2m^3+8m-2m^2=0 | | -2y^2-48y=70 | | -7x+4=-3x-12 | | 4+4x-7=4x+3-x | | 7(6k+1)=-37-2k | | 5k^2+48k+64=0 | | -3d+4+9d=-8 | | 3(34a+3)+6=87 |

Equations solver categories