How do you solve #x^2-7x=5# using the quadratic formula?

1 Answer
Aug 8, 2015

Answer:

#x = (7+sqrt(69))/2#
or
#x = (7-sqrt(69))/2#

Explanation:

Given #x^2-7x =5#

Re-writing in standard form:
#color(white)("XXXX")##1x^2-7x-5 = 0#

The general standard form for a quadratic is
#color(white)("XXXX")##ax^2+bx+c = 0#

The quadratic formula tells us that the solution for an equation in the general form is:
#color(white)("XXXX")##x = (-b+-sqrt(b^2-4ac))/(2a)#

Base on the re-written form of the given equation:
#a=1##color(white)("XXXX")##b=-7##color(white)("XXXX")##c=-5#

So the solution is
#color(white)("XXXX")##x = (7+-sqrt((-7)^2-4(1)(-5)))/(2(1)#

#color(white)("XXXX")##color(white)("XXXX")##=(7+-sqrt(69))/2#