select the correct answer.\nwhat are the solutions of this quadratic equation?\n4x² + 3 = 4x + 2\na. x =…

Explanation:

Step1: Rearrange the equation to standard form

First, rewrite $4x^{2}+3 = 4x + 2$ as $4x^{2}-4x + 1=0$. Here we subtract $4x$ and $2$ from both sides.

Step2: Identify coefficients for quadratic formula

For a quadratic equation $ax^{2}+bx + c = 0$, in our case $a = 4$, $b=-4$, $c = 1$.

Step3: Apply the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

Substitute the values: $x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4\times4\times1}}{2\times4}=\frac{4\pm\sqrt{16 - 16}}{8}=\frac{4\pm0}{8}=\frac{1}{2}$.

Answer:

A. $x=\frac{1}{2}$