Question

I need help with this math question on my assignment

Answer 1

we have the expression

x^2+9x+20

Complete the square

equate the expression to zero

x^2+9x+20=0

group terms

(x^2+9x)=-20

x^2+9x+(9/2)^2-(9/2)^2=20

x^2+9x+(9/2)^2=20+(9/2)^2

Rewrite as perfect squares

(x+9/2)^2=-20+81/4

(x+9/2)^2=1/4

take square root on both sides

`(x+(9)/(2))=\pm\sqrt[]{(1)/(4)}`

simplify

`\begin{gathered} x+(9)/(2)=\pm(1)/(2) \\ x=-(9)/(2)\pm(1)/(2) \end{gathered}`

the values of x are

x=-4 and x=-5

therefore

the given expression in factored form is

x^2+9x+20=(x+4)(x+5)

another way to find out the factored form

the formula to solve a quadratic equation of the form

ax^2+bx+c=0

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In this problem we have

x^2+9x+20=0

so

a=1

b=9

c=20

substitute in the formula

`x=\frac{-9\pm\sqrt[]{9^2-4(1)(20)}}{2(1)}`
`\begin{gathered} x=\frac{-9\pm\sqrt[]{1}}{2} \\ x=(-9\pm1)/(2) \\ x=(-9+1)/(2)=-4 \\ x=(-9-1)/(2)=-5 \end{gathered}`

the values of x are

x=-4 and x=-5

therefore

the factored form is

(x+4)(x+5)