Answer:
[tex]x=\dfrac{-i\sqrt2}{2} ,\dfrac{i\sqrt2}{2}[/tex]
Step-by-step explanation:
Quadratic Formula
The quadratic formula uses the coefficients in a quadratic's standard form (ax + bx + c) to find its solutions.
[tex]\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\hrulefill[/tex]
Solving the Problem
We're given the equation
5x² + 1 = 3x².
For a quadratic to be in the standard form its value should equal 0.
So, we must rearrange the equation,
2x²+1 = 0 (subtract 3x² both sides).
Here, a = 2; b = 0; c = 1.
So,
[tex]\dfrac{-(0) \pm \sqrt{(0)^2-4(2)(1)} }{2(2)}=\dfrac{\pm \sqrt{-8} }{4}[/tex]
[tex]= \dfrac{\pm (\sqrt{-1} \cdot \sqrt8)}{4} =\dfrac{\pm(i \cdot 2\sqrt2)}{4} =\boxed{\dfrac{\pm i\sqrt2}{2}}[/tex].
