Answer:
Step-by-step explanation:
Factor it by first setting it equal to 0:
[tex]4x^2+9=0[/tex] Now subtract 9 from both sides:
[tex]4x^2=-9[/tex] Divide both sides by 4:
[tex]x^2=-\frac{9}{4}[/tex] Then take the square root of both sides:
x = ±[tex]\sqrt{-\frac{9}{4} }[/tex] , which of course is not allowed. Therefore, we have to allow for the imaginary numbers in this solution. Knowing that,
x = ±[tex]\sqrt{-1*\frac{9}{4} }[/tex] is an equivalent radicand, we can now replace -1 with its imaginary counterpart:
x = ±[tex]\sqrt{i^2*\frac{9}{4} }[/tex]
Each one of the elements in the radicand are perfect squares, so we simplify as follows:
x = ±[tex]\frac{3}{2}i[/tex]
And there you go!
