1. **State the problem:** Solve the equation $x^2 - x2 = 36$. 2. **Rewrite the equation:** The term $x2$ is ambiguous, but it likely means $2x$. So the equation becomes: $$x^2 - 2x = 36$$ 3. **Bring all terms to one side:** $$x^2 - 2x - 36 = 0$$ 4. **Use the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Here, $a=1$, $b=-2$, and $c=-36$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-2)^2 - 4(1)(-36) = 4 + 144 = 148$$ 6. **Find the roots:** $$x = \frac{-(-2) \pm \sqrt{148}}{2(1)} = \frac{2 \pm \sqrt{148}}{2}$$ 7. **Simplify the square root:** $$\sqrt{148} = \sqrt{4 \times 37} = 2\sqrt{37}$$ 8. **Final solutions:** $$x = \frac{2 \pm 2\sqrt{37}}{2} = 1 \pm \sqrt{37}$$ **Answer:** $$x = 1 + \sqrt{37} \quad \text{or} \quad x = 1 - \sqrt{37}$$