# Video: Solving Nonmonic Quadratic Equations with Imaginary Roots

Solve the equation 5𝑥² + 1 = − 319.

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### Video Transcript

Solve the equation five 𝑥 squared plus one equals negative 319.

We can begin by solving this equation just as we would any other, by performing a series of inverse operations. We’ll start by subtracting one from both sides of the equation. Five 𝑥 squared plus one minus one is simply five 𝑥 squared. And negative 319 minus one is negative 320.

Next, we divide through by five. And we see that 𝑥 squared is equal to negative 64. Our final step is to find the square root of both sides of the equation. The square root of 𝑥 squared is 𝑥. And remember, we can take both the positive and negative roots of negative 64. And we see that 𝑥 is equal to plus or minus the square root of negative 64.

At this point, we choose to rewrite negative 64 as 64 multiplied by negative one. And we then see that the square root of negative 64 is the same as the square root of 64 multiplied by the square root of negative one. The square root of negative one though is 𝑖, and the square root of 64 is eight. And we finished solving our equation. 𝑥 has two solutions. It’s eight 𝑖 and negative eight 𝑖.