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.
