Question

3.) find the solutions by completing the square
$x^2 + 2x - 35 = 0$

Explanation:

Step1: Move constant to right

$x^2 + 2x = 35$

Step2: Complete the square

Take half of 2, square it: $(\frac{2}{2})^2 = 1$. Add to both sides:
$x^2 + 2x + 1 = 35 + 1$
$(x + 1)^2 = 36$

Step3: Take square roots

$x + 1 = \pm\sqrt{36}$
$x + 1 = \pm6$

Step4: Solve for x

Case 1: $x + 1 = 6 \implies x = 5$
Case 2: $x + 1 = -6 \implies x = -7$

Answer:

The solutions are $x = 5$ and $x = -7$.