The quadratic formula is:
[tex]x=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
and
[tex]x=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
Let's identify our a, b, and c values:
a: -1
b: 1
c: 12
Plug in the values for a, b, and c into the equation. Let's do the first equation:
[tex]x=\frac{-1+\sqrt{(1)^2-4(-1)(12)}}{2(-1)}[/tex]
Simplify everything in the radical:
[tex]x=\frac{-1+\sqrt{49}}{-2}[/tex]
Simplify the radical:
[tex]x=\frac{-1+7}{-2}[/tex]
Combine like terms:
[tex]x=\frac{6}{-2}[/tex]
Simplify:
[tex]x=-3[/tex]
This is one solution, now, let's solve for the other equation:
Since when simplified, everything is the same except the subtraction sign, we can skip the simplification again and change the sign to subtraction:
[tex]x=\frac{-1-7}{-2}[/tex]
Combine like terms:
[tex]x=\frac{-8}{-2}[/tex]
Simplify:
[tex]x=4[/tex]
Your final answers are:
[tex]x=-3[/tex]
[tex]x=4[/tex]
[tex]ax^2+bx+c=0[/tex]
[tex]H(t)=-t^2+t+12[/tex]
a = -1; b = +1; c = 12
Quadratic Formula: [tex]\frac{-b±\sqrt{b^2-4ac} }{2a} \\ \\ \frac{-(1)±\sqrt{(1)^2-4(-1)(12)} }{2(-1)} \\ \\ \frac{-1±\sqrt{(1)+4(12)} }{-2}\\ \\ \frac{-1±\sqrt{(1)+48} }{-2}\\ \\ \frac{-1±\sqrt{49} }{-2}\\ \\ \frac{-1±7 }{-2}\\ \\ \frac{-1+7 }{-2}...and...\frac{-1-7 }{-2}\\ \\ -3...and...+4[/tex]
This should be your final answer. So sorry about the capital A if it's in the whole work I did here. I can't get rid of it whenever I put plus and minus sign. I remember saying this and they had a solution for it on Brainly but I forgot what that was...
