When the square of a certain number is decreased by 6 times the number, the result is -9. What is the number?

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Answer 1 · 2016-10-12T16:25:36

The number is #3#.

#1.#Set up an equation

#x^2-6x=-9#

#2.#Set the equation equal to #0#

#x^2-6x=-9#
#x^2-6x+9=0# #larr#This is a quadratic equation!

#3.# Solve for the unknown

Personally, I prefer the quadratic formula over factorising, so...
Plug in and simplify!

#x=(-b+-sqrt(b^2-4ac))/(2a)#

#x=(6+-sqrt(-6^2– 4xx1xx9))/(2xx1)#

#x=(6+-sqrt(36 – 36))/(2)#

#x=(6+-sqrt(0))/(2)#

#x=6/2#

#x=3#