10=k(4k-1)

Simple and best practice solution for 10=k(4k-1) 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 10=k(4k-1) equation:


Simplifying
10 = k(4k + -1)

Reorder the terms:
10 = k(-1 + 4k)
10 = (-1 * k + 4k * k)
10 = (-1k + 4k2)

Solving
10 = -1k + 4k2

Solving for variable 'k'.

Reorder the terms:
10 + k + -4k2 = -1k + k + 4k2 + -4k2

Combine like terms: -1k + k = 0
10 + k + -4k2 = 0 + 4k2 + -4k2
10 + k + -4k2 = 4k2 + -4k2

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

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.5 + -0.25k + k2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.25k + 2.5 + k2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.25k + k2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.25k + k2 = 0 + 2.5
-0.25k + k2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.25k + k2 = 2.5

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.25k + 0.25 + k2 = 2.5 + 0.25

Reorder the terms:
0.25 + -0.25k + k2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + -0.25k + k2 = 2.75

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(k + 0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

k + 0.5 = 1.658312395 Simplifying k + 0.5 = 1.658312395 Reorder the terms: 0.5 + k = 1.658312395 Solving 0.5 + k = 1.658312395 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 1.658312395 + -0.5 k = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 k = 1.158312395 Simplifying k = 1.158312395

Subproblem 2

k + 0.5 = -1.658312395 Simplifying k + 0.5 = -1.658312395 Reorder the terms: 0.5 + k = -1.658312395 Solving 0.5 + k = -1.658312395 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -1.658312395 + -0.5 k = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 k = -2.158312395 Simplifying k = -2.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.158312395, -2.158312395}

See similar equations:

| 16x^2+36= | | -3(x+u)+(3u-6x)= | | -2x+9=29 | | 16(80)+8(320-80)=10(320) | | 2s+5s=63 | | x^2-19x-84=0 | | x-2-4-x= | | 16x+8(320-x)=10(320) | | 20+2x=3y | | 16x+8(320-x)=15 *320 | | 16x+8(320-x)=10 *320 | | (x+4)+(2x+5)+6x=180 | | -(3x-3)-x= | | 3b^2-6b-45=0 | | -3(-6w+v)+(5v+w)= | | (x+6)(x+8)=0 | | 6p^2+5pq-6q^2= | | 7(x-3)-17=9x-2(x-8) | | 8(n+3)(n+7)=0 | | 3t=-27 | | -7(2b+1)+(15b-9)=0 | | 1.2q-3.9-5.7q=-5.5q-1.8 | | -8x^2+3+11x^2-14-5x= | | 0=24-10x-x^2 | | 12n^2-47n+45= | | 8a=40 | | 0.55x+0.05(18-x)=0.10(89) | | y=2x-5(13) | | x+600-10x=177 | | x+x+19+x+21=150 | | 12z-16+16=7+16 | | w(2w-14)=60 |

Equations solver categories