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Answer:
D = 0; one real root
Step-by-step explanation:
Discriminant Formula:
[tex] \displaystyle \large{D = {b}^{2} - 4ac}[/tex]
First, arrange the expression or equation in ax^2+bx+c = 0.
[tex] \displaystyle \large{ {x}^{2} + 6x = - 9}[/tex]
Add both sides by 9.
[tex] \displaystyle \large{ {x}^{2} + 6x + 9 = - 9 + 9} \\ \displaystyle \large{ {x}^{2} + 6x + 9 = 0}[/tex]
Compare the coefficients so we can substitute in the formula.
[tex] \displaystyle \large{a {x}^{2} + bx + c = {x}^{2} + 6x + 9 }[/tex]
Substitute a = 1, b = 6 and c = 9 in the formula.
[tex] \displaystyle \large{D = {6}^{2} - 4(1)(9)} \\ \displaystyle \large{D = 36 - 36} \\ \displaystyle \large{D = 0}[/tex]
Since D = 0, the type of solution is one real root.