Question 448327
From {{{2x^2-25}}} we can see that {{{a=2}}}, {{{b=0}}}, and {{{c=-25}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(0)^2-4(2)(-25)}}} Plug in {{{a=2}}}, {{{b=0}}}, and {{{c=-25}}}



{{{D=0-4(2)(-25)}}} Square {{{0}}} to get {{{0}}}



{{{D=0--200}}} Multiply {{{4(2)(-25)}}} to get {{{(8)(-25)=-200}}}



{{{D=0+200}}} Rewrite {{{D=0--200}}} as {{{D=0+200}}}



{{{D=200}}} Add {{{0}}} to {{{200}}} to get {{{200}}}



So the discriminant is {{{D=200}}}



Since the discriminant is greater than zero, this means that there are two real solutions. These solutions are distinct (ie different from one another).