r^2-10r+(-5)=-17

Simple and best practice solution for r^2-10r+(-5)=-17 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+(-5)=-17 equation:


Simplifying
r2 + -10r + (-5) = -17
r2 + -10r + -5 = -17

Reorder the terms:
-5 + -10r + r2 = -17

Solving
-5 + -10r + r2 = -17

Solving for variable 'r'.

Reorder the terms:
-5 + 17 + -10r + r2 = -17 + 17

Combine like terms: -5 + 17 = 12
12 + -10r + r2 = -17 + 17

Combine like terms: -17 + 17 = 0
12 + -10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -10r + -12 + r2 = 0 + -12

Reorder the terms:
12 + -12 + -10r + r2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -10r + r2 = 0 + -12
-10r + r2 = 0 + -12

Combine like terms: 0 + -12 = -12
-10r + r2 = -12

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 = -12 + 25

Reorder the terms:
25 + -10r + r2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + -10r + r2 = 13

Factor a perfect square on the left side:
(r + -5)(r + -5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(r + -5) equal to 3.605551275 and -3.605551275.

Subproblem 1

r + -5 = 3.605551275 Simplifying r + -5 = 3.605551275 Reorder the terms: -5 + r = 3.605551275 Solving -5 + r = 3.605551275 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 = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + r = 3.605551275 + 5 r = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 r = 8.605551275 Simplifying r = 8.605551275

Subproblem 2

r + -5 = -3.605551275 Simplifying r + -5 = -3.605551275 Reorder the terms: -5 + r = -3.605551275 Solving -5 + r = -3.605551275 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 = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + r = -3.605551275 + 5 r = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 r = 1.394448725 Simplifying r = 1.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. r = {8.605551275, 1.394448725}

See similar equations:

| 3x+2[y+-1[3x+-1(z+-2y)]+z]+-2y=0 | | 36x^2-1x=0 | | 34x+73y=1 | | 2x-1/3-6x-2/5=1/3 | | X^5+x+1=0 | | solve(3-w)(2w+7)=0 | | 11-4x=23 | | t+24=16 | | -2-13= | | 3(4m+5)-12=2m+7 | | 13-3x=-2 | | 10p-13=4p-4 | | 4x^2+22x-53500=0 | | 2(3q+1)=5q-3 | | 4.3q-2.1-4.8q=-1.5q-2.7 | | 5p+7+9p=-21forp | | 2p-3=4/10(3p-4) | | x+x+3x+3x=22 | | 3n+19=25-3n | | 38.72-23.19= | | 38.72-23.19=31.18 | | 9.1+18.1+13.4+v=62.5 | | 10.8+8.7+w=31.9 | | 10.8+8.7+w=31.0 | | 10.8+8.7=31.9 | | pd=ps | | q+18.3=20 | | y=4x*-3 | | 6.3+f=10.5 | | x=144^1/2 | | 4x/4-x=3 | | 10.3x-6x=-2.3 |

Equations solver categories