1. **State the problem:** Write the quadratic expression $x^2 + 6x - 7$ in the form $(x + a)^2 + b$ where $a$ and $b$ are integers. 2. **Recall the formula:** To complete the square for a quadratic expression $x^2 + bx + c$, use the identity: $$x^2 + bx + c = (x + \frac{b}{2})^2 + \left(c - \left(\frac{b}{2}\right)^2\right)$$ This means we take half of the coefficient of $x$, square it, and add and subtract it inside the expression. 3. **Apply to the given expression:** Here, $b = 6$ and $c = -7$. Calculate half of $b$: $$\frac{6}{2} = 3$$ Square it: $$3^2 = 9$$ 4. **Rewrite the expression:** $$x^2 + 6x - 7 = (x + 3)^2 - 9 - 7$$ Simplify the constants: $$-9 - 7 = -16$$ So, $$x^2 + 6x - 7 = (x + 3)^2 - 16$$ 5. **Final answer:** The expression in the form $(x + a)^2 + b$ is: $$(x + 3)^2 - 16$$