Step 1: Divide the entire equation by the coefficient of $x^2$. The given equation is $2x^2 - 13x + 15 = 0$. Divide by 2: $$x^2 - \frac{13}{2}x + \frac{15}{2} = 0$$ Step 2: Move the constant term to the right side of the equation. $$x^2 - \frac{13}{2}x = -\frac{15}{2}$$ Step 3: Take half of the coefficient of the $x$ term, square it, and add it to both sides of the equation. The coefficient of $x$ is $-\frac{13}{2}$. Half of this is $\frac{1}{2} \times \left(-\frac{13}{2}\right) = -\frac{13}{4}$. Square this value: $\left(-\frac{13}{4}\right)^2 = \frac{169}{16}$. Add $\frac{169}{16}$ to both sides: $$x^2 - \frac{13}{2}x + \frac{169}{16} = -\frac{15}{2} + \frac{169}{16}$$ Step 4: Factor the left side as a perfect square trinomial and simplify the right side. The left side factors as $\left(x - \frac{13}{4}\right)^2$. For the right side, find a common denominator: $$-\frac{15}{2} + \frac{169}{16} = -\frac{15 \times 8}{2 \times 8} + \frac{169}{16} = -\frac{120}{16} + \frac{169}{16} = \frac{169 - 120}{16} = \frac{49}{16}$$ So the equation becomes: $$\left(x - \frac{13}{4}\right)^2 = \frac{49}{16}$$ Step 5: Take the square root of both sides. $$x - \frac{13}{4} = \pm\sqrt{\frac{49}{16}}$$ $$x - \frac{13}{4} = \pm\frac{7}{4}$$ Step 6: Solve for $x$. $$x = \frac{13}{4} \pm \frac{7}{4}$$ This gives two possible solutions: $$x_1 = \frac{13}{4} + \frac{7}{4} = \frac{20}{4} = 5$$ $$x_2 = \frac{13}{4} - \frac{7}{4} = \frac{6}{4} = \frac{3}{2}$$ The solutions are $\boxed{x=5 \text{ or } x=\frac{3}{2}}$. Send me the next one 📸