SOLUTION: I'm not sure how to do this, and i need some help. consider the equation x^2+2x=7. Prove that this equation has two real roots.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I'm not sure how to do this, and i need some help. consider the equation x^2+2x=7. Prove that this equation has two real roots.      Log On


   

Question 155043: I'm not sure how to do this, and i need some help.
consider the equation x^2+2x=7. Prove that this equation has two real roots.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B2x=7 Start with the given equation


x%5E2%2B2x-7=0 Subtract 7 from both sides


Solved by pluggable solver: Computing the Discriminant


From x%5E2%2B2x-7 we can see that a=1, b=2, and c=-7



D=b%5E2-4ac Start with the discriminant formula.



D=%282%29%5E2-4%281%29%28-7%29 Plug in a=1, b=2, and c=-7



D=4-4%281%29%28-7%29 Square 2 to get 4



D=4--28 Multiply 4%281%29%28-7%29 to get %284%29%28-7%29=-28



D=4%2B28 Rewrite D=4--28 as D=4%2B28



D=32 Add 4 to 28 to get 32



Since the discriminant is greater than zero, this means that there are two real solutions.