solve for x in the equation 2x² - 5x + 1 = 3.\n○ x = 5/2 ± √29/2\n○ x = 5/2 ± √41/4\n○ x = 5/4 ± √29/2\n○ x…

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $2x^{2}-5x + 1=3$ as $2x^{2}-5x - 2=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 2$, $b=-5$, $c=-2$.

Step2: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 2$, $b=-5$, $c=-2$ into it. Calculate $b^{2}-4ac=(-5)^{2}-4\times2\times(-2)=25 + 16=41$.

Step3: Find the values of x

$x=\frac{-(-5)\pm\sqrt{41}}{2\times2}=\frac{5\pm\sqrt{41}}{4}$.

Answer:

$x=\frac{5}{4}\pm\frac{\sqrt{41}}{4}$