Question

What are the values of x in the equation 4x2 4x – 3 = 0? x = –1.5, 0.5 x = –0.5, –1.5 x = x =?

Answer 1

Answer:

The values of x are

$x=-1.5\ , 0.5$

Step-by-step explanation:

we have

$4x^{2}+4x-3=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$4x^{2}+4x=3$

Factor the leading coefficient

$4(x^{2}+x)=3$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$4(x^{2}+x+.25)=3+1$

$4(x^{2}+x+.25)=4$

$(x^{2}+x+.25)=1$

Rewrite as perfect squares

$(x+0.5)^{2}=1$

Square root both sides

$x+0.5=(+/-)1$

$x=-0.5(+/-)1$

$x=-0.5+1=0.5$

$x=-0.5-1=-1.5$

Answer 2

4x^2+ 4x – 3 = 0

Using Quadratic Formula:

x = [-4 + sqrt(16+48)]/8
or
x = [-4 - sqrt(16+48)]/8

Solving First equation:
x = [-4 + sqrt(16+48)]/8
   = -4+8/8
   = 0.5

Solving Second equation:
x = [-4 - sqrt(16+48)]/8
   = - 4 - 8 /8
   = -12/8
   = -1.5