3k^2+13k-52=0

Simple and best practice solution for 3k^2+13k-52=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+13k-52=0 equation: 


Simplifying
3k2 + 13k + -52 = 0

Reorder the terms:
-52 + 13k + 3k2 = 0

Solving
-52 + 13k + 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'.
-17.33333333 + 4.333333333k + k2 = 0

Move the constant term to the right:

Add '17.33333333' to each side of the equation.
-17.33333333 + 4.333333333k + 17.33333333 + k2 = 0 + 17.33333333

Reorder the terms:
-17.33333333 + 17.33333333 + 4.333333333k + k2 = 0 + 17.33333333

Combine like terms: -17.33333333 + 17.33333333 = 0.00000000
0.00000000 + 4.333333333k + k2 = 0 + 17.33333333
4.333333333k + k2 = 0 + 17.33333333

Combine like terms: 0 + 17.33333333 = 17.33333333
4.333333333k + k2 = 17.33333333

The k term is 4.333333333k.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333k + 4.694444446 + k2 = 17.33333333 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333k + k2 = 17.33333333 + 4.694444446

Combine like terms: 17.33333333 + 4.694444446 = 22.027777776
4.694444446 + 4.333333333k + k2 = 22.027777776

Factor a perfect square on the left side:
(k + 2.166666667)(k + 2.166666667) = 22.027777776

Calculate the square root of the right side: 4.693375947

Break this problem into two subproblems by setting 
(k + 2.166666667) equal to 4.693375947 and -4.693375947.


Subproblem 1
k + 2.166666667 = 4.693375947

Simplifying
k + 2.166666667 = 4.693375947

Reorder the terms:
2.166666667 + k = 4.693375947

Solving
2.166666667 + k = 4.693375947

Solving for variable 'k'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + k = 4.693375947 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + k = 4.693375947 + -2.166666667
k = 4.693375947 + -2.166666667

Combine like terms: 4.693375947 + -2.166666667 = 2.52670928
k = 2.52670928

Simplifying
k = 2.52670928


Subproblem 2
k + 2.166666667 = -4.693375947

Simplifying
k + 2.166666667 = -4.693375947

Reorder the terms:
2.166666667 + k = -4.693375947

Solving
2.166666667 + k = -4.693375947

Solving for variable 'k'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + k = -4.693375947 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + k = -4.693375947 + -2.166666667
k = -4.693375947 + -2.166666667

Combine like terms: -4.693375947 + -2.166666667 = -6.860042614
k = -6.860042614

Simplifying
k = -6.860042614


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.52670928, -6.860042614}

See similar equations:

| 3log(2x+2)=12 | | (a+-7)= | | 81*5/6 | | -34+3x=46+8x | | 4x-1/4=3/2 | | -2/5=4 | | 3ln(2x+2)=12 | | 4n+6=-4n+2n | | x-12=(-23) | | 0.83+p=2 | | 5=z/4=3 | | 2x+6=11x+0.5 | | 4y=(-2) | | 10x+9-13x=-9 | | 4.1=5.9-.9x | | 20x+10=20x+10 | | x-7/2=5 | | 11x-39=21+8x | | 3y^2-300=0 | | .7(x+300)=0.78x-358 | | 0(2y)=36 | | 12=2t+6 | | 4(3y-1)3(2y)=6 | | 4(5x+7-8x)+2=-18 | | 1/x=10/6 | | (-22)=18-1/3x | | 7sinx+2=3 | | -(z+s)=-14 | | 4x/3-5=(-37) | | .01(x+21)-.21=.01(8x+21) | | 4cos(4x)=3 | | -4(5t-5)+3t=2t-2 |

Equations solver categories