Question

1. write two equivalent forms for the given equation $x^2 + 14x - 51 = 0$

$\square$=0 (factored form)
$(\square)^2=\square$

Explanation:

Step1: Factor the quadratic equation

Find two numbers: product=-51, sum=14 → 17 and -3.
So $x^2 +14x -51=(x+17)(x-3)$

Step2: Complete the square

$x^2 +14x =51$, add $(\frac{14}{2})^2=49$ to both sides:
$x^2 +14x +49=51+49 → (x+7)^2=100$

Answer:

$(x + 17)(x - 3)$
$x + 7$; $100$