SOLUTION: I need help with a quadratic Equation 2x^2=90 How do i use the quadratic formula if there is no middle term? Thank you

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Question 220696: I need help with a quadratic Equation 2x^2=90
How do i use the quadratic formula if there is no middle term?
Thank you

Found 2 solutions by tutor_paul, jim_thompson5910:
Answer by tutor_paul(519) (Show Source):
You can put this solution on YOUR website!
you can still use the quadratic formula if you want, just make the b term zero. however it's easier not to use it in a case like this...
2x^2=90
x^2=45
x=+/-sqrt(45)
x=+/-3sqrt(5)
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Good Luck,
tutor_paul@yahoo.com

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given equation

Subtract 90 from both sides

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like notice , , and )

Plug in a=2, b=0, and c=-90

Square 0 to get 0

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or