How do you solve #x^2+7x=-3# using the quadratic formula?

1 Answer
Jul 5, 2015

Answer:

Rewrite the given formula in standard form, then apply the quadratic formula for roots to get #x=-1/2# or #x=-13/2#

Explanation:

#x^2+7x=-3#
#color(white)("XXXX")#is equivalent to
#x^2+7x+3=0#
#color(white)("XXXX")#which is a quadratic in standard form
#color(white)("XXXX")##color(white)("XXXX")##ax^2+bx+c=0#
#color(white)("XXXX")#whose roots are given by the quadratic formula:
#color(white)("XXXX")##color(white)("XXXX")##x = (-b+-sqrt(b^2-4ac))/(2a)#

Using #a=1#, #b=7#, and #c=3#
we have
#color(white)("XXXX")##x= (-7+-sqrt(7^2-4(1)(3)))/(2(1)#

#color(white)("XXXX")##x = (-7+-sqrt(36))/2#

#color(white)("XXXX")##x = (-7+-6)/2#

#x=-1/2# or #x=-13/2#