First, we compare the given quadratic equation 2x² - 7x + 3 = 0 with the standard form of a quadratic equation, ax² + bx + c = 0. This allows us to identify the values of the coefficients a, b, and c.

First, we compare the given quadratic equation 2x² - 7x + 3 = 0 with the standard form of a quadratic equation, ax² + bx + c = 0. This allows us to identify the values of the coefficients a, b, and c.

Solve the quadratic equation $2x^2 - 7x + 3 = 0$ using the quadratic formula.

Answer: The solutions are $x = 3$ and $x = \frac{1}{2}$ .

Step-by-step solution

Step 1: Identify coefficients

First, we compare the given quadratic equation $2x^2 - 7x + 3 = 0$ with the standard form of a quadratic equation, $ax^2 + bx + c = 0$ . This allows us to identify the values of the coefficients $a$ , $b$ , and $c$ .

Step 2: State the quadratic formula

The quadratic formula is used to find the roots of any quadratic equation. It provides a direct way to calculate the values of $x$ once the coefficients $a$ , $b$ , and $c$ are known.

Step 3: Substitute values into the formula

Now, we substitute the identified values of $a=2$ , $b=-7$ , and $c=3$ into the quadratic formula. This is the crucial step before performing the arithmetic calculations.

Step 4: Simplify the expression

Next, we simplify the expression under the square root and perform the multiplication in the denominator. The square root of 25 is 5, which further simplifies the expression.

Step 5: Calculate the two roots

Finally, we calculate the two possible values for $x$ by considering both the positive and negative signs of the square root. This gives us the two roots of the quadratic equation.

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Solve the quadratic equation 2x2−7x+3=02x^2 - 7x + 3 = 02x2−7x+3=0 using the quadratic formula.