Question 245918
1. write a quadratic equation having the given numbers as solutions
5, only solution 
(x-5)*(x-5) = 0
{{{x^2 - 10x + 25 = 0}}}
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2. complete the square. then write the trinomial square in factored form.
x^2-3x
x^2 - 3x + 2.25
= (x - 1.5)^2
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3. solve by applying the quadratic formula
2x^2+7x+3=0
*[invoke solve_quadratic_equation 2,7,3]
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4. use the discriminant to determine whether the following equations have solutions that are two different rational solutions; two different irrational solutions; exactly one rational solution, or two different imaginary solutions.
10-5a^2=7a+9 
5a^2 + 7a - 1 = 0
The online solver covers the Discriminant well.
*[invoke solve_quadratic_equation 5,7,-1]