4x-(1/2)x^(-1/2)

Simple and best practice solution for 4x-(1/2)x^(-1/2) 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 4x-(1/2)x^(-1/2) equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

4*x-((1/2)*x^(-1/2)) = 0

4*x+(-1/2)*x^(-1/2) = 0

4*x-1/2*x^(-1/2) = 0

t_1 = x^(1/2)

4*t_1^2-1/2*t_1^-1 = 0

(4*t_1^3-1/2*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(4*t_1^3-1/2*t_1^0) = 0

t_1^1

4*t_1^3-1/2 = 0

4*t_1^3-1/2 = 0 // * 0

{ 1, -1 }

1

t_1 = 1

8*t_1^3-1 = 7

1

-1

t_1 = -1

8*t_1^3-1 = -9

-1

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8 }

1/2

t_1

1/2

8*t_1^3-1 = 0

1/2

t_1-1/2

8*t_1^2+4*t_1+2

8*t_1^3-1

t_1-1/2

4*t_1^2-8*t_1^3

4*t_1^2-1

2*t_1-4*t_1^2

2*t_1-1

1-2*t_1

0

8*t_1^2+4*t_1+2 = 0

DELTA = 4^2-(2*4*8)

DELTA = -48

DELTA < 0

t_1 in { 1/2} 

t_1 = 1/2

x^(1/2)-(1/2) = 0

x^(1/2)-1/2 = 0

1*x^(1/2) = 1/2 // : 1

x^(1/2) = 1/2

x^(1/2) = 1/2 // ^ 2

x = 1/4

x = 1/4

See similar equations:

| 9n-3=2n+46 | | 2h=7 | | 5x+3xy=4y+15 | | -31/2=-1/2 | | -8x+12=2x+10 | | 5x-2(10x-3)=4(7-5x)-35x+2 | | 5/6(12x+24)=-13x+4 | | 18x+1/2= | | 16n=19n | | (x-1)(x-1)+5=0 | | 27a^3/19b^21 | | 120(15-x)=180(x) | | Y=x^3+6x^2-9x-11 | | 3x+7(3x-7)=71 | | 6x+6=3+8x-7 | | 3/4x-9/513/15-1/4x | | 0.10x+0.05(2-x)=0.10(-8) | | 5x-3-x-4x=10 | | 2(2x-3)=26 | | 13x+6=14x-2 | | 50=(x)(x)/(0.2-x)(0.2-x) | | 2(4x-16)=18(x-4) | | 2y=6+12 | | 7x+1=7(x-7) | | 6sin(x)= | | 32x+8=40 | | 5+35x=21x+11 | | 7x-3y+12z= | | 2/3x+6=1/4x-3 | | 5x+3x-8-x=-1 | | 5a-2a=51 | | 11.1x-2.4=-6.5x+6 |

Equations solver categories