r^2-23r-10=0

Simple and best practice solution for r^2-23r-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^2-23r-10=0 equation:


Simplifying
r2 + -23r + -10 = 0

Reorder the terms:
-10 + -23r + r2 = 0

Solving
-10 + -23r + 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 + -23r + 10 + r2 = 0 + 10

Reorder the terms:
-10 + 10 + -23r + r2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -23r + r2 = 0 + 10
-23r + r2 = 0 + 10

Combine like terms: 0 + 10 = 10
-23r + r2 = 10

The r term is -23r.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23r + 132.25 + r2 = 10 + 132.25

Reorder the terms:
132.25 + -23r + r2 = 10 + 132.25

Combine like terms: 10 + 132.25 = 142.25
132.25 + -23r + r2 = 142.25

Factor a perfect square on the left side:
(r + -11.5)(r + -11.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(r + -11.5) equal to 11.926860442 and -11.926860442.

Subproblem 1

r + -11.5 = 11.926860442 Simplifying r + -11.5 = 11.926860442 Reorder the terms: -11.5 + r = 11.926860442 Solving -11.5 + r = 11.926860442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + r = 11.926860442 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + r = 11.926860442 + 11.5 r = 11.926860442 + 11.5 Combine like terms: 11.926860442 + 11.5 = 23.426860442 r = 23.426860442 Simplifying r = 23.426860442

Subproblem 2

r + -11.5 = -11.926860442 Simplifying r + -11.5 = -11.926860442 Reorder the terms: -11.5 + r = -11.926860442 Solving -11.5 + r = -11.926860442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + r = -11.926860442 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + r = -11.926860442 + 11.5 r = -11.926860442 + 11.5 Combine like terms: -11.926860442 + 11.5 = -0.426860442 r = -0.426860442 Simplifying r = -0.426860442

Solution

The solution to the problem is based on the solutions from the subproblems. r = {23.426860442, -0.426860442}

See similar equations:

| 7w+2w=36 | | 5/7x-4/3=3x+1/2 | | -4+d=-7 | | 1/3z+1/6=5+1/6 | | -3(7n-6)+3= | | 5/7x-4/3 | | -7z=-7 | | 3(8-x)=5(2x-3) | | 4x^2+42x-72=0 | | .5x+4=.6666666667x | | 72x^4-12x^3=0 | | 5n+2=3n-8 | | 4lnx=-12 | | 3x-1(x+4)=10 | | 5d+28=11d+9d-2 | | 18x-2=99-21+4x | | y=-3/2(-2)-15 | | 2w^2-w-120=0 | | -3.5=-x | | U-5=8 | | 2.75-7.75(5-2x)=25 | | 14x+7-29=7x+12-3x | | x^2+2x-135= | | 4/x=12/28 | | 12=p+7 | | -3x-2y=30 | | 13=u+10 | | 6a+24=7a+5a | | 1-x/5 | | 6p=5p+3 | | 12=y-9 | | 3x+15*2=119 |

Equations solver categories