1. Problem: Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. Step 1: Identify coefficients: $$a=1$$, $$b=-5$$, $$c=6$$. 3. Step 2: Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 4. Step 3: Calculate discriminant: $$\Delta = b^2 - 4ac = (-5)^2 - 4(1)(6) = 25 - 24 = 1$$. 5. Step 4: Find roots: $$x = \frac{-(-5) \pm \sqrt{1}}{2(1)} = \frac{5 \pm 1}{2}$$. 6. Step 5: Calculate each root: $$x_1 = \frac{5 + 1}{2} = 3$$ $$x_2 = \frac{5 - 1}{2} = 2$$. 7. Final answer: The solutions are $$x=3$$ and $$x=2$$. --- 1. Problem: Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. Step 1: Factor numerator: $$2x^2 - 8 = 2(x^2 - 4)$$. 3. Step 2: Recognize difference of squares: $$x^2 - 4 = (x-2)(x+2)$$. 4. Step 3: Rewrite expression: $$\frac{2(x-2)(x+2)}{4x}$$. 5. Step 4: Simplify constants: $$\frac{2}{4} = \frac{1}{2}$$. 6. Step 5: Final simplified expression: $$\frac{(x-2)(x+2)}{2x}$$. --- 1. Problem: Solve for $$y$$: $$3y - 7 = 11$$. 2. Step 1: Add 7 to both sides: $$3y = 11 + 7 = 18$$. 3. Step 2: Divide both sides by 3: $$y = \frac{18}{3} = 6$$. Final answer: $$y=6$$.