Answer:
x = -2, x = 9
Step-by-step explanation:
Given quadratic equation:
[tex]x^2-7x-18=0[/tex]
To factor a quadratic in the form ax²+bx+c, first find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -18=-18[/tex]
[tex]\implies b=-7[/tex]
Therefore, the two numbers are: -9 and 2.
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-9x+2x-18=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-9)+2(x-9)=0[/tex]
Factor out the common term (x - 9):
[tex]\implies (x+2)(x-9)=0[/tex]
Apply the zero-product property:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-9=0 \implies x=9[/tex]
Therefore, the solutions to the given quadratic equation are:
