Question

1b) solve the equation $x^2 + 7x - 18 = 0$ by factoring.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to $-18$ and add up to $7$. The numbers are $9$ and $-2$ because $9\times(-2) = -18$ and $9 + (-2)=7$.

Step2: Factor the quadratic

Using the numbers from Step 1, we factor the quadratic equation $x^{2}+7x - 18 = 0$ as $(x + 9)(x - 2)=0$.

Step3: Solve for x

Set each factor equal to zero:

• For $x + 9 = 0$, we get $x=-9$.
• For $x - 2 = 0$, we get $x = 2$.

Answer:

The solutions are $x = -9$ and $x = 2$.