Question

Find the solution set of the following quadratic equations using the quadratic formula.

1.) x^2 - 7x + 9 = 0
2.) 3x^2 + 10x = -3​​

Answer 1

1)
`x_1=\frac{7+√(13)}2\,,\quad x_2=\frac{7-√(13)}2`

2)
`x_1=-\frac13\,,\quad x_2=-3`

Explanation:

1)

`x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=(-b\pm√(b^2-4ac))/(2a)=(-(-7)\pm√((-7)^2-4\cdot1\cdot9))/(2\cdot1)=\frac{7\pm√(49-36)}2\\\\x_1=\frac{7+√(13)}2\,,\quad x_2=\frac{7-√(13)}2`

2)

`3x^2 + 10x=-3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\\\\x=(-b\pm√(b^2-4ac))/(2a)=(-10\pm√(10^2-4\cdot3\cdot3))/(2\cdot3)= \frac{-10\pm√(100-36)}6\\\\x_1=\frac{-10+√(64)}6=\frac{-10+8}6=-\frac13\,,\qquad x_2=\frac{-10-8}6=-3`