k^2+5k=4

Simple and best practice solution for k^2+5k=4 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 k^2+5k=4 equation: 


Simplifying
k2 + 5k = 4

Reorder the terms:
5k + k2 = 4

Solving
5k + k2 = 4

Solving for variable 'k'.

Reorder the terms:
-4 + 5k + k2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 5k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5k + 4 + k2 = 0 + 4

Reorder the terms:
-4 + 4 + 5k + k2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5k + k2 = 0 + 4
5k + k2 = 0 + 4

Combine like terms: 0 + 4 = 4
5k + k2 = 4

The k term is 5k.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5k + 6.25 + k2 = 4 + 6.25

Reorder the terms:
6.25 + 5k + k2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5k + k2 = 10.25

Factor a perfect square on the left side:
(k + 2.5)(k + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(k + 2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
k + 2.5 = 3.201562119

Simplifying
k + 2.5 = 3.201562119

Reorder the terms:
2.5 + k = 3.201562119

Solving
2.5 + k = 3.201562119

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = 3.201562119 + -2.5
k = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
k = 0.701562119

Simplifying
k = 0.701562119


Subproblem 2
k + 2.5 = -3.201562119

Simplifying
k + 2.5 = -3.201562119

Reorder the terms:
2.5 + k = -3.201562119

Solving
2.5 + k = -3.201562119

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = -3.201562119 + -2.5
k = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
k = -5.701562119

Simplifying
k = -5.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.701562119, -5.701562119}

See similar equations:

| 5-2(x-3)= | | 4y*(4+y^2)=0 | | 23s-10=65s-94 | | 81=25x^2 | | (x/8)-(13/4)=(x/4)+4 | | (3b+5)(b-4)=0 | | u^2-8+12=0 | | 4x^2-92x+168=0 | | 2(d-5)-9=-5 | | X^2-30x-104=0 | | 1.25=(217)/(13.2)(13.2) | | 584=100(200p)+4p | | x=900+1600 | | x^2*(9x^5-32)*(x+16)/4 | | y^4+10y^2-11=0 | | 5r-10r+2r+r= | | 40(40)= | | (4/x-1)=(13/x+8) | | 30(30)= | | x+4+3x-8=180 | | 2u-2u+u=20 | | 3(3)= | | cos(x-10)=-0.5 | | 4(x+1)-3= | | 3(23)= | | m+2mx+mx^2=4x-12 | | 17r-17r+r+1=13 | | (5x-3)-2x=-30 | | 262=(217+x)/(13.2-x)(13.2-x) | | -6a+4a-5-7= | | 60=17b | | 11d/7-2d=16 |

Equations solver categories