Answer:
The solution set is x={2,-12}
Step-by-step explanation:
Given: [tex]x^2+10x=24[/tex]
Using complete square to solve for x
[tex]x^2+10x=24[/tex]
Add both side square of half of coefficient of x ( i,e 25)
[tex]x^2+10x+25=24+25[/tex]
[tex](x+5)^2=49[/tex] [tex]\because a^2+2ab+b^2=(a+b)^2[/tex]
Taking square root both sides
[tex]\sqrt{(x+5)^2}=\pm \sqrt{49}[/tex]
[tex]x+5=\pm7[/tex]
[tex]x=-5\pm7[/tex]
[tex]x=-5+7[/tex] and [tex]x=-5-7[/tex]
[tex]x=2,-12[/tex]
Hence, The solution set is x={2,-12}
