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How do you solve the quadratic using the quadratic formula given #9x^2-11=6x#?

Answer 1

Chloe Alexander

We put our equation into standard form, then use the quadratic equation to find

#x=(1 +- 2sqrt(3))/3 ~= 1.49, -0.821#

To use the quadratic formula, we must first put our equation into the standard form:

#ax^2+bx+c=0#

We can do this by subtracting #6x# from both sides of our equation yielding:

#9x^2-6x-11=0#

This allows us to match up the values

#a=9, b=-6" "# and #" "c=-11#

Then we use the quadratic formula:

#x = (-b +- sqrt(b^2-4ac))/(2a)=(6 +- sqrt(36-4*9*(-11)))/18#

#x=(6 +- sqrt(432))/18 = (1 +- 2sqrt(3))/3#

#x~= 1.49, -0.821#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.