To solve the equation by factoring, we want to set the equation to zero. In order to have the equation equal to zero, we want to add both sides by 36.

8x²=-36 [add both sides by 36]

8x²+36=0

When it comes to factoring, we want to pull out numbers or variables that are common in each term.

8x²+36=0 [take out a 4 in each term]

4(2x²+9)=0

It may seem that 2x²+9 can be factored further, it actually can't. This tells us that the factored form of the equation is 4(2x²+9)=0.

To solve the equation, we want to find the value of x. We already know the graph does not cross the x-axis because the y-intercept or vertex is (0,9).

4(2x²+9)=0 [divide both sides by 4]

2x²+9=0 [subtract both sides by 9]

2x²=-9 [divide both sides by 2]

x²=-9/2 [square root both sides]

$x=\sqrt{-\frac{9}{2} }$ or $x=i\frac{3\sqrt{2} }{2}$

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