Solve each equation in Exercises 47–64 by completing the square. $2 x^{2} - 7 x + 3 = 0$

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Start with the given quadratic equation: $2x^2 - 7x + 3 = 0$.

Divide the entire equation by the coefficient of $x^2$, which is 2, to make the coefficient of $x^2$ equal to 1: $x^2 - \frac{7}{2}x + \frac{3}{2} = 0$.

Move the constant term to the right side of the equation: $x^2 - \frac{7}{2}x = -\frac{3}{2}$.

To complete the square, take half of the coefficient of $x$, which is $-\frac{7}{2}$, divide it by 2 to get $-\frac{7}{4}$, then square it to get $\left(-\frac{7}{4}\right)^2 = \frac{49}{16}$. Add this value to both sides of the equation: $x^2 - \frac{7}{2}x + \frac{49}{16} = -\frac{3}{2} + \frac{49}{16}$.

Rewrite the left side as a perfect square trinomial: $\left(x - \frac{7}{4}\right)^2 = -\frac{3}{2} + \frac{49}{16}$. Then simplify the right side by finding a common denominator and combining the terms.

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