r^2-10r=13

Simple and best practice solution for r^2-10r=13 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=13 equation:


Simplifying
r2 + -10r = 13

Reorder the terms:
-10r + r2 = 13

Solving
-10r + r2 = 13

Solving for variable 'r'.

Reorder the terms:
-13 + -10r + r2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -10r + 13 + r2 = 0 + 13

Reorder the terms:
-13 + 13 + -10r + r2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -10r + r2 = 0 + 13
-10r + r2 = 0 + 13

Combine like terms: 0 + 13 = 13
-10r + r2 = 13

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 = 13 + 25

Reorder the terms:
25 + -10r + r2 = 13 + 25

Combine like terms: 13 + 25 = 38
25 + -10r + r2 = 38

Factor a perfect square on the left side:
(r + -5)(r + -5) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(r + -5) equal to 6.164414003 and -6.164414003.

Subproblem 1

r + -5 = 6.164414003 Simplifying r + -5 = 6.164414003 Reorder the terms: -5 + r = 6.164414003 Solving -5 + r = 6.164414003 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 = 6.164414003 + 5 Combine like terms: -5 + 5 = 0 0 + r = 6.164414003 + 5 r = 6.164414003 + 5 Combine like terms: 6.164414003 + 5 = 11.164414003 r = 11.164414003 Simplifying r = 11.164414003

Subproblem 2

r + -5 = -6.164414003 Simplifying r + -5 = -6.164414003 Reorder the terms: -5 + r = -6.164414003 Solving -5 + r = -6.164414003 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 = -6.164414003 + 5 Combine like terms: -5 + 5 = 0 0 + r = -6.164414003 + 5 r = -6.164414003 + 5 Combine like terms: -6.164414003 + 5 = -1.164414003 r = -1.164414003 Simplifying r = -1.164414003

Solution

The solution to the problem is based on the solutions from the subproblems. r = {11.164414003, -1.164414003}

See similar equations:

| (20+2x)(40+2x)=1500 | | 3xy^2(x-y)-10x^2y^2+12xy^3= | | 9×1/4 | | 0.9x+0.1(2000-x)=191 | | B=4x+10 | | 5(x+1)-x=4x+1 | | 7x+2-2x=32 | | 2x+x+3=x | | (4-y)(4+y)= | | 5y(4y+2)=148 | | 2x^2+52x+62=0 | | 11=4r-41 | | X/8=168 | | 8a^2-64a=0 | | 5x-1+2x+7=-3x-14 | | 2(7+2w)+2w=110 | | 5x-108=11x | | 4b^2=8 | | 2+5x+4=26 | | -2(2x-3)=-4(x+1)-2 | | 3+(8)= | | 0=-19x^2+38x+5 | | 9x^2-63x-702=0 | | 31+x+4=90 | | 5045x+6000=5795 | | (7x+4)(x-7)= | | C^2=144-17c | | 24w+42=20w+62 | | (3x-15)+(5x-23)=90 | | 4d^2+104d=116 | | 80=21/2x-7/2 | | 6u^2-19u-7=0 |

Equations solver categories