1. **State the problem:** Solve the quadratic equation $X^2 + 8X + 10 = 30$ using the factorising method. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$X^2 + 8X + 10 - 30 = 0$$ which simplifies to $$X^2 + 8X - 20 = 0$$ 3. **Identify coefficients:** Here, $a = 1$, $b = 8$, and $c = -20$. 4. **Find two numbers that multiply to $a \times c = 1 \times (-20) = -20$ and add to $b = 8$:** These numbers are 10 and -2 because $10 \times (-2) = -20$ and $10 + (-2) = 8$. 5. **Rewrite the middle term using these numbers:** $$X^2 + 10X - 2X - 20 = 0$$ 6. **Group terms:** $$(X^2 + 10X) + (-2X - 20) = 0$$ 7. **Factor each group:** $$X(X + 10) - 2(X + 10) = 0$$ 8. **Factor out the common binomial:** $$(X - 2)(X + 10) = 0$$ 9. **Set each factor equal to zero and solve for $X$:** $$X - 2 = 0 \implies X = 2$$ $$X + 10 = 0 \implies X = -10$$ **Final answer:** The solutions are $X = 2$ and $X = -10$.