How do you solve #n^2 - 17=64# using the quadratic formula?

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Answer 1 · 2016-08-05T21:02:09

#n=+-9#

#n^2-17=64#
#n^2=64+17#
#n^2=81#
#n=sqrt81#
#n=+-9#

Answer 2 · 2016-08-05T21:04:52

#n=+-9#

Write as #n^2-81#

As it is insisted we use the quadratic formula write as:

#n^2+0n-81=0#

#=>n=(-0+-sqrt(0^2-4(1)(-81)))/(2(1))#

#=>n=+-sqrt(324)/2=(+-18)/2 = +-9#

Answer 3 · 2016-08-05T22:06:58

#n=9, -9#

#n^2-17=64#

Subtract #64# from both sides of the equation.

#n^2-17-64=0#

Simplify.

#n^2-81#

This equation is in the form of a quadratic equation, #ax^2+bx+c=0#, where #a=1#, #b=0#, and #c=-81#.

The quadratic formula can be used to solve this quadratic equation.

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

Substitute #n# for #x# and plug the known values into the formula.

#n=(-0+-sqrt(0^2-4*1*-81))/(2*1)#

Simplify.

#n=(+-sqrt(324))/(2)#

Simplify.

#n=+-18/2#

Simplify.

#n=+-9#

Solve for #n#.

#n=9#

#n=-9#