Answer:
The factors are [tex](x-7)[/tex] and [tex](x+2)[/tex]
Step-by-step explanation:
we have
[tex]x^{2} -5x-14[/tex]
To find the factors equate the equation to zero
[tex]x^{2} -5x-14=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2} -5x=14[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2} -5x+6.25=14+6.25[/tex]
[tex]x^{2} -5x+6.25=20.25[/tex]
Rewrite as perfect squares
[tex](x-2.5)^{2}=20.25[/tex]
[tex](x-2.5)=(+/-)\sqrt{20.25}[/tex]
[tex](x-2.5)=(+/-)4.5[/tex]
[tex]x=2.5(+/-)4.5[/tex]
[tex]x=2.5+4.5=7[/tex]
[tex]x=2.5-4.5=-2[/tex]
therefore
[tex]x^{2} -5x-14=(x-7)(x+2)[/tex]
using a graphing tool see the attached figure
The factors of the quadratic equation are the x-intercepts (values of x when the value of the function is equal to zero)
