3k^2-2k+3k-21=0

Simple and best practice solution for 3k^2-2k+3k-21=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 3k^2-2k+3k-21=0 equation: 


Simplifying
3k2 + -2k + 3k + -21 = 0

Reorder the terms:
-21 + -2k + 3k + 3k2 = 0

Combine like terms: -2k + 3k = 1k
-21 + 1k + 3k2 = 0

Solving
-21 + 1k + 3k2 = 0

Solving for variable 'k'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-7 + 0.3333333333k + k2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 0.3333333333k + 7 + k2 = 0 + 7

Reorder the terms:
-7 + 7 + 0.3333333333k + k2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 0.3333333333k + k2 = 0 + 7
0.3333333333k + k2 = 0 + 7

Combine like terms: 0 + 7 = 7
0.3333333333k + k2 = 7

The k term is 0.3333333333k.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333k + 0.02777777779 + k2 = 7 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333k + k2 = 7 + 0.02777777779

Combine like terms: 7 + 0.02777777779 = 7.02777777779
0.02777777779 + 0.3333333333k + k2 = 7.02777777779

Factor a perfect square on the left side:
(k + 0.1666666667)(k + 0.1666666667) = 7.02777777779

Calculate the square root of the right side: 2.65099562

Break this problem into two subproblems by setting 
(k + 0.1666666667) equal to 2.65099562 and -2.65099562.


Subproblem 1
k + 0.1666666667 = 2.65099562

Simplifying
k + 0.1666666667 = 2.65099562

Reorder the terms:
0.1666666667 + k = 2.65099562

Solving
0.1666666667 + k = 2.65099562

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + k = 2.65099562 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + k = 2.65099562 + -0.1666666667
k = 2.65099562 + -0.1666666667

Combine like terms: 2.65099562 + -0.1666666667 = 2.4843289533
k = 2.4843289533

Simplifying
k = 2.4843289533


Subproblem 2
k + 0.1666666667 = -2.65099562

Simplifying
k + 0.1666666667 = -2.65099562

Reorder the terms:
0.1666666667 + k = -2.65099562

Solving
0.1666666667 + k = -2.65099562

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + k = -2.65099562 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + k = -2.65099562 + -0.1666666667
k = -2.65099562 + -0.1666666667

Combine like terms: -2.65099562 + -0.1666666667 = -2.8176622867
k = -2.8176622867

Simplifying
k = -2.8176622867


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.4843289533, -2.8176622867}

See similar equations:

| 4.3x=0.215 | | -8+3y=-10 | | t(t-14)=72 | | 12x+30=-10 | | 13(a-5)=-5-8 | | 1/12b=5 | | Y=4m^2-m+7m^4+2r^2 | | 48=w/7.5 | | 1/5x+2=0 | | 4m^2-m+7m^4+2r^2=y | | x-28=-1 | | 8+d/5=23 | | -5x-y=-21 | | x-23=-1 | | (u-3)(u+2)=0 | | 10x-1-9x=3 | | 2x-20=I | | 2x-3-4-5=345-47x | | x(8-x)+1whenx=-4 | | 9.4k+k=37.5 | | 3=6(-2x+1)+2(6x+1) | | 0.3-5=7 | | 8x-(6x+9)=9x-16 | | Y=4m^2-m+7m+2r^2 | | 12n+8-11n-4=11 | | 8.5x-4.3=3.3+3.5 | | 12x^3+32x^2+x-10=0 | | 4(x-2)+2(x+1)=x-60 | | y=4(-2)-5 | | 7+4(2x-2)=4x-5 | | y-3+5=15 | | 90=-6(2x-1) |

Equations solver categories