4k^2-16k+9=0

Simple and best practice solution for 4k^2-16k+9=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 4k^2-16k+9=0 equation:


Simplifying
4k2 + -16k + 9 = 0

Reorder the terms:
9 + -16k + 4k2 = 0

Solving
9 + -16k + 4k2 = 0

Solving for variable 'k'.

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

Divide each side by '4'.
2.25 + -4k + k2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -4k + -2.25 + k2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -4k + k2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -4k + k2 = 0 + -2.25
-4k + k2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-4k + k2 = -2.25

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = -2.25 + 4

Reorder the terms:
4 + -4k + k2 = -2.25 + 4

Combine like terms: -2.25 + 4 = 1.75
4 + -4k + k2 = 1.75

Factor a perfect square on the left side:
(k + -2)(k + -2) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(k + -2) equal to 1.322875656 and -1.322875656.

Subproblem 1

k + -2 = 1.322875656 Simplifying k + -2 = 1.322875656 Reorder the terms: -2 + k = 1.322875656 Solving -2 + k = 1.322875656 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + k = 1.322875656 + 2 k = 1.322875656 + 2 Combine like terms: 1.322875656 + 2 = 3.322875656 k = 3.322875656 Simplifying k = 3.322875656

Subproblem 2

k + -2 = -1.322875656 Simplifying k + -2 = -1.322875656 Reorder the terms: -2 + k = -1.322875656 Solving -2 + k = -1.322875656 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + k = -1.322875656 + 2 k = -1.322875656 + 2 Combine like terms: -1.322875656 + 2 = 0.677124344 k = 0.677124344 Simplifying k = 0.677124344

Solution

The solution to the problem is based on the solutions from the subproblems. k = {3.322875656, 0.677124344}

See similar equations:

| 10x-3=47 | | -(5y+4)-(-4y-7)=-5 | | 9x^2-140=0 | | 7+2p-4=8p+8-5p | | 6(4x-6)=2(12x+3) | | 5x^2-50+120=0 | | 7+15r-5=8r+52-3r | | .5(4+x)= | | 4s+13s=119 | | 2x+12=68x-6x | | x/3=-29 | | 10-8x=82-36x | | y=48x-12x^3 | | y=48x-12x^2 | | 2.8q-2.7-4.2q=-2.4q-1.7 | | 7x+3x=18 | | z-27=-13 | | 7h+5h-3=15 | | -(5y+4)-(-4y-7)=-1 | | 2-1=y | | 7(s-4)=-3+2s | | x^2+5x-40=0 | | 5x-2(6+7x)=15 | | y-25=-38 | | 12(2x-3)=4(6x+9) | | p+-5=7 | | x^2+2x-103=-4 | | 8q-5=16-(-q) | | 6+13p-3=9p+53-6p | | -4-(-3p)=-5p-8 | | 5(2x-4)=3x-(6x-19) | | -(7y+1)-(-6y-8)=8 |

Equations solver categories