Sure! Let's solve the quadratic equation step-by-step.
Given the equation:
[tex]\[ 4x^2 + 3 = 4x + 2 \][/tex]
First, we want to set the equation to zero by bringing all terms to one side:
[tex]\[ 4x^2 + 3 - 4x - 2 = 0 \][/tex]
Combine like terms:
[tex]\[ 4x^2 - 4x + 1 = 0 \][/tex]
This is a standard quadratic equation of the form [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = 4 \)[/tex], [tex]\( b = -4 \)[/tex], and [tex]\( c = 1 \)[/tex].
To solve the quadratic equation, we can use the quadratic formula, which is given by:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Now substitute [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] into the quadratic formula:
[tex]\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 4 \cdot 1}}{2 \cdot 4} \][/tex]
[tex]\[ x = \frac{4 \pm \sqrt{16 - 16}}{8} \][/tex]
[tex]\[ x = \frac{4 \pm \sqrt{0}}{8} \][/tex]
[tex]\[ x = \frac{4 \pm 0}{8} \][/tex]
[tex]\[ x = \frac{4}{8} \][/tex]
[tex]\[ x = \frac{1}{2} \][/tex]
Therefore, the solution to the quadratic equation is:
[tex]\[ x = \frac{1}{2} \][/tex]
So, the correct answer is:
A. [tex]\( x = \frac{1}{2} \)[/tex]
