Write $x^2 + 6x - 7$ in the form $(x + a)^2 + b$ where $a$ and $b$ are integers. - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 3

To rewrite the quadratic expression $x^2 + 6x - 7$, we first complete the square. We focus on the terms $x^2 + 6x$.

1. Take half of the coefficient of $x$, which is $6$. Half of $6$ is $3$, and squaring it gives us $3^2 = 9$.
2. Rewrite the expression as: $x^2 + 6x = (x + 3)^2 - 9$
3. Now substitute back into the original expression: $x^2 + 6x - 7 = (x + 3)^2 - 9 - 7$
4. Combine the constants: $-9 - 7 = -16$.

Thus, we have: $(x + 3)^2 - 16$