Answer:
Solving the equation for all real solutions in simplest form.
[tex]z^2 - 12z +9= -3[/tex] we get [tex]\mathbf{z=10.9\: or\: z=1.1}[/tex]
Step-by-step explanation:
We need to solve the equation for all real solutions in simplest form.
[tex]z^2 - 12z +9= -3[/tex]
First simplifying the equation:
[tex]z^2 - 12z +9+3= -3+3\\z^2 - 12z +12= 0[/tex]
Now, we can solve the equation using quadratic formula:
[tex]z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
we have a = 1, b=-12 and c=12
Putting values in formula and finding values of x
[tex]z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\z=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)}}{2(1)}\\z=\frac{12\pm\sqrt{144-48}}{2}\\z=\frac{12\pm\sqrt{96}}{2}\\z=\frac{12\pm9.8}{2}\\z=\frac{12+9.8}{2}\:or\:z=\frac{12-9.8}{2}\\z=10.9\:or\:z=1.1[/tex]
So, we get value of z: z=10.9 or z=1.1
Solving the equation for all real solutions in simplest form.
[tex]z^2 - 12z +9= -3[/tex] we get [tex]\mathbf{z=10.9\: or\: z=1.1}[/tex]
