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If S is between R and T, RT=24, RS=x^2+8, and ST= 3x+6

how to find the value of X and if S is the midpoint or not (please show how you got the answer)



Answer :

R•----S•-----•T
The total (RT) is 24. So you need to find the segments that make up RT. (RS & ST) Set up your equation by plugging in what you know. We know RS is x²+8. We also know that ST is 3x+6. And that RT is 24. So, RS + ST = RT. x²+8 (RS) + 3x+6 (ST) = 24 (RT). Then just combine like terms, and solve for x. Then plug x back into each equation (such as RS & ST) to figure out what they equal.
[tex]|RT|=24;\ |RS|=x^2+8;\ |ST|=3x+6\\\\|RT|=|RS|+|ST|\\\\(x^2+8)+(3x+6)=24\\x^2+3x+14-24=0\\x^2+3x-10=0\\x^2+5x-2x-10=0\\x(x+5)-2(x+5)=0\\(x+5)(x-2)=0\iff x+5=0\ or\ x-2=0\\\boxed{x=-5\ or\ x=2}[/tex]
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