Question 174866
{{{x^2+11x+121=x+96}}} Start with the given equation.



{{{x^2+11x+121-1x-96=0}}} Subtract x from both sides. Subtract 96 from both sides.



{{{x^2+10x+25=0}}} Combine like terms.


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Now let's find the discriminant of {{{x^2+10x+25}}}:



From {{{x^2+10x+25}}} we can see that {{{a=1}}}, {{{b=10}}}, and {{{c=25}}}



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



{{{D=(10)^2-4(1)(25)}}} Plug in {{{a=1}}}, {{{b=10}}}, and {{{c=25}}}



{{{D=100-4(1)(25)}}} Square {{{10}}} to get {{{100}}}



{{{D=100-100}}} Multiply {{{4(1)(25)}}} to get {{{(4)(25)=100}}}



{{{D=0}}} Subtract {{{100}}} from {{{100}}} to get {{{0}}}



So the discriminant is 0.



Note: Since the discriminant is equal to zero, this means that there is one real solution.