1. **State the problem:** Solve the quadratic equation $x^2 + 25 = 10x + 4$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$x^2 + 25 - 10x - 4 = 0$$ Simplify: $$x^2 - 10x + 21 = 0$$ 3. **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, $a=1$, $b=-10$, and $c=21$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-10)^2 - 4 \times 1 \times 21 = 100 - 84 = 16$$ 5. **Find the roots:** $$x = \frac{-(-10) \pm \sqrt{16}}{2 \times 1} = \frac{10 \pm 4}{2}$$ 6. **Calculate each root:** - For the plus sign: $$x = \frac{10 + 4}{2} = \frac{14}{2} = 7$$ - For the minus sign: $$x = \frac{10 - 4}{2} = \frac{6}{2} = 3$$ 7. **Final answer:** The solutions to the equation are $x=7$ and $x=3$.