Question

solve using any method. 32. $8x - 1 = 4x^2$

Explanation:

Step1: Rearrange to standard quadratic form

$4x^2 - 8x + 1 = 0$

Step2: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, $a=4$, $b=-8$, $c=1$.
$$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(4)(1)}}{2(4)}$$

Step3: Simplify the discriminant

$\sqrt{64 - 16}=\sqrt{48}=4\sqrt{3}$

Step4: Simplify the full expression

$$x=\frac{8\pm4\sqrt{3}}{8}=\frac{2\pm\sqrt{3}}{2}$$

Answer:

$x=\frac{2+\sqrt{3}}{2}$ and $x=\frac{2-\sqrt{3}}{2}$