SOLUTION: Use the discriminant to determine the kinds of numbers that will satisfy the equation 5x = x^2 - 3. Do not solve

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Question 65840This question is from textbook An Incremental Development
: Use the discriminant to determine the kinds of numbers that will satisfy the equation 5x = x^2 - 3. Do not solve This question is from textbook An Incremental Development

Answer by 303795(602) About Me  (Show Source):
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Rearrange the equation to get it in the ax%5E2%2Bbx%2Bc=0 form.
5x=x%5E2-3
Subtract 5x from each side.
5x-5x=x%5E2-5x-3
x%5E2-5x-3=0
The discriminant is found using the formula
b%5E2-4%2Aa%2Ac
In this example a=1, b=-5 and c=-3
%28-5%29%5E2-4%2A1%2A%28-3%29
25-%28-12%29
=37
The number is positive so there will be two real solutions to the equation.
(a value of zero implies one solution and a negative value implies no real solution but two solutions involving complex numbers.)