Question

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

Answer 1

The solution set of the equation are (2,0) and (-12,0)

Explanation:

Given : Equation
`x^2+10x=24`

To find : Solve equation by completing the square ?

Solution :

The general form of quadratic equation is
`ax^2+bx+c=0`

So,
`x^2+10x-24=0`

To complete the square we add and subtract
`((b)/(2))^2`

i.e.
`((b)/(2))^2=((10)/(2))^2=5^2`

Applying in equation,

`x^2+10x-24+5^2-5^2=0`

Re-writ equation as,

`x^2+2* 5* x+5^2-24-25=0`

Apply
`a^2+2ab+b^2=(a+b)^2`

`(x+5)^2-49=0`

`(x+5)^2=49`

Taking root both side,

`x+5=\pm √(49)`

`x+5=\pm 7`

`x+5=7` or
`x+5=-7`

`x=2` or
`x=-12`

Therefore, the solution set of the equation are (2,0) and (-12,0)

Answer 2

The correct answer is C!!!

I hope this helps you out, have an amazing day

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