Question

Find the real solutions of the quadratic equation $4x^2-4x+1=0$.

Short answer

The real solution of the quadratic equation is $x=\frac{1}{2}$.

Step-by-step solution

Step 1. By method of quadratic formula.

The roots of the quadratic equation of the form $a{x}^2+bx+c=0$where $a\ne 0$can be evaluated by using the quadratic formula shown below.

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Step 2. Find roots of quadratic equation by quadratic formula.

The given quadratic equation is $4x^2-4x+1=0$whose roots can be evaluated by quadratic formula as shown below.

$$\begin{gathered} x=\frac{-\left(-4\right)\pm \sqrt{{\left(-4\right)}^2-4\left(4\right)\left(1\right)}}{2\left(4\right)} \\ =\frac{4\pm \sqrt{0}}{8} \\ =\frac{4}{8} \\ =\frac{1}{2} \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

The real solution of the equation is $x=\frac{1}{2}$.