Question

4x^2 +24x+35=0

Answer 1

you need to factor...

Answer 2

x = \[-24 \pm \sqrt{24^2-4(4)(35) }\]
\[/2(4)\]

Answer 3

good call, use the quadratic equation for that. You could, however, factor that. 35 has the following primes: 5, 7. 24 has the following primes: 2,2,2,3, and 4 has two primes, 2,2. Don't think this will factor into easy integers, so just use quadratic equation here.

Answer 4

Doesn't look like it factors easily, so use completing the square:

\[4x ^2+24x +35 = 0\]
(Divide by the x-squared coeficient)
\[x ^2+6x +35/4 = 0\]
(Move the constant term to the other side)
\[x ^2+6x = -35/4\]
(Take half the coeficient of the x term, square it, and add to both sides)
\[x ^2+6x +3^2 = -35/4 +3^2\]
(Now the left side of the equation is a perfect square, and factors easily)
\[(x +3)^2 = -35/4 +9\]
(take the square root of each side)
\[x +3 = \pm\sqrt{-35/4 +9}\]
(now just move the three over, and you're done)
\[x =-3 \pm\sqrt{-35/4 +9}\]

Answer 5

Ends up reducing to -5/2 and -7/2