Question

solve the equation.

\\w^2 - 5w + 3 = 0\\

the solution set is \\{\quad\\}.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify coefficients

Identify the coefficients \(a\), \(b\), and \(c\) from the quadratic equation \(w^2 - 5w + 3 = 0\):

$$a = 1, \quad b = -5, \quad c = 3$$

Step 2: Apply the quadratic formula

Substitute the values into the quadratic formula:

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

$$w = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(3)}}{2(1)}$$

Step 3: Simplify the expression

Simplify the terms inside and outside the radical:

$$w = \frac{5 \pm \sqrt{25 - 12}}{2}$$

$$w = \frac{5 \pm \sqrt{13}}{2}$$

Answer:

$$\frac{5 + \sqrt{13}}{2}, \frac{5 - \sqrt{13}}{2}$$