Question 373133
Use the discriminant,
{{{D=b^2-4ac}}}
{{{D=b^2-4(4)(25)}}}
{{{D=b^2-400}}}
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When {{{D>0}}}, two real solutions.
When {{{D>0}}} and equals a perfect square(1,4,9,16,...), then the solutions are rational solutions. 
When {{{D>0}}} and does not equal a perfect square(1,4,9,16,...), then the solutions are irrational solutions. 
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When {{{D=0}}}, one real solution.
When {{{D=0}}} and equals a perfect square(1,4,9,16,...), then the solution is a rational solution. 
When {{{D=0}}} and does not equal a perfect square(1,4,9,16,...), then the solutions is an irrational solution. 
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When {{{D<0}}}, two complex solutions.
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Now solve for {{{b}}} in each of those cases.