4k^2+2k=1

Simple and best practice solution for 4k^2+2k=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 4k^2+2k=1 equation:


Simplifying
4k2 + 2k = 1

Reorder the terms:
2k + 4k2 = 1

Solving
2k + 4k2 = 1

Solving for variable 'k'.

Reorder the terms:
-1 + 2k + 4k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2k + 4k2 = 0

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

Divide each side by '4'.
-0.25 + 0.5k + k2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5k + 0.25 + k2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5k + k2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5k + k2 = 0 + 0.25
0.5k + k2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.5k + k2 = 0.25

The k term is 0.5k.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5k + 0.0625 + k2 = 0.25 + 0.0625

Reorder the terms:
0.0625 + 0.5k + k2 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + 0.5k + k2 = 0.3125

Factor a perfect square on the left side:
(k + 0.25)(k + 0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(k + 0.25) equal to 0.559016994 and -0.559016994.

Subproblem 1

k + 0.25 = 0.559016994 Simplifying k + 0.25 = 0.559016994 Reorder the terms: 0.25 + k = 0.559016994 Solving 0.25 + k = 0.559016994 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + k = 0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + k = 0.559016994 + -0.25 k = 0.559016994 + -0.25 Combine like terms: 0.559016994 + -0.25 = 0.309016994 k = 0.309016994 Simplifying k = 0.309016994

Subproblem 2

k + 0.25 = -0.559016994 Simplifying k + 0.25 = -0.559016994 Reorder the terms: 0.25 + k = -0.559016994 Solving 0.25 + k = -0.559016994 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + k = -0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + k = -0.559016994 + -0.25 k = -0.559016994 + -0.25 Combine like terms: -0.559016994 + -0.25 = -0.809016994 k = -0.809016994 Simplifying k = -0.809016994

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.309016994, -0.809016994}

See similar equations:

| -5(x)=5x-3 | | 5x+9=-19-2x | | 2(2x-5)+2(7)=24 | | 3(g+4)+-8=-19 | | 2m+4(m-3)=-24 | | 10-x+3=-3+15x-2x+2x | | 2y=-2.3 | | 7(6x^2-5x-8)=0 | | 2x+5(x+2)=171 | | -4+5x=-5x+86 | | 2.1x+1.4x-4.6=2.2 | | (4-v)(5v+9)=0 | | 22-11/35 | | 5y=-4.7 | | P=150+3.5m | | 3(n^2+8n+8)=0 | | -3(4-x)=10-25+5x | | 0.6/0.02 | | 3.5k+2-2.5k=8 | | n+3n+16=116 | | -91=-7(m+8) | | 12=a-8 | | g=2d+f | | 6400=p+.06p | | 12.5/3.14 | | 2v^2-9v-9=v^2-6v+9 | | 2x+4-x+1= | | 2(2x-7)-2=2(x-3)+4 | | 11/2x=3 | | 9x^2-3x-174=0 | | (13*9.72-36)=180 | | (2m^2-3m+7)(7m-8)=0 |

Equations solver categories