Question

Solve x2 – 5x – 24 = 0 by completing the square.Question 13 options:A) x = 6 and x = –4B) x = 3 and x = –8C) x = –3 and x = 8D) x = –6 and x = –4

Answer 1

Given:

`x^2-5x-24=0`

First, let us keep the x terms on the left side and move the constant to the right side of the equation through adding 24 on both sides.

`x^2-5x-24+24=0+24`
`x^2-5x=24`

Next, we will take the half of the x term, 5x, and square it.

`((5)/(2))^2=(25)/(4)`

And then, we will add this to both sides of the equation.

`x^2-5x+(25)/(4)=24+(25)/(4)`

Then, we will rewrite the left side of the equation as a perfect square

`(x-(5)/(2))^2=(121)/(4)`

Take the square root of both sides

`\sqrt[]{(x-(5)/(2))^2}=\sqrt[]{(121)/(4)}`
`x-(5)/(2)=\pm(11)/(2)`

Solve for x (1)

`x=(5)/(2)+(11)/(2)`
`x=(16)/(2)`
`x=8`

Solve for x (2)

`x=(5)/(2)-(11)/(2)`
`x=(-6)/(2)`
`x=-3`

Now, we know that the values of x are -3 and 8, therefore, the answer would be C. x=-3 and x=8.