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=(7+√(13))/(2)\,,\qquad x_2=(7-√(13))/(2)`

2.)
`x_1=-\frac13\,,\qquad x_2=-3`

Explanation:

1.)

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

2.)

`3x^2 + 10x = -3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b=10\,,\ c = 3\\\\\\x=(-b-√(b^2-4ac))/(2a)\\\\x=(-10\pm√(10^2-4\cdot3\cdot3))/(2\cdot3)=(-10\pm√(100-36))/(6)=(-10\pm√(64))/(6)\\\\x_1=(-10+8)/(6)=\frac{-2}6=-\frac13\,,\qquad x_2=(-10-8)/(6)=(-18)/(6)=-3`