In cases such as this, when solving quadratic equations with non-real solutions, you learned that you can use the imaginary unit i to write the solutions of the quadratic equation as complex numbers.

And standard form, of course, is the form ax squared plus bx plus c is equal to 0. Take note that we be simplifying complex numbers — so if you need a review of how to rewrite the square root of a negative number as an imaginary number, now is a good time.

And so our left hand side becomes 2x squared minus 6x plus 5 is equal to-- and then on our right hand side, these two characters cancel out, and we just are left with 0.

So we verified that both of these complex roots, satisfy this quadratic equation. Now what I want to do is a verify that these work.

So the square root of negative 4, that is the same thing as 2i. The Quadratic Formula When solving a quadratic equation set equal to zero, as shown below, the solution sx, to the quadratic equation can be found using the quadratic formula.

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Quadratic Equations with Complex Solutions