Video: Solving Simple Cubic Equations

Solve 𝑥³ + 5 = 9.

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Video Transcript

Solve 𝑥 cubed plus five equals nine.

Well, the first thing we wanna do when solving an equation in this form is actually get the 𝑥 term on its own. So to do that, the first thing we’re gonna do is actually subtract five from each side of our equation. So that’s gonna give us 𝑥 cubed is equal to four. Because if we have plus five minus five, that’s gonna be zero. And if we have nine minus five, we get four.

Okay, great. So now, we’ve got 𝑥 cubed equals four. So now, what we’re gonna do is actually inverse of cube because we’ve got 𝑥 cubed. So what we’re gonna do is cube-root each side. So therefore, we can say that 𝑥 — because if you cube-root a cube, you’re just left with the original value or in this case 𝑥 — is gonna be equal to the cube root of four. So we’re actually gonna leave our answer in this form because we don’t wanna lose any accuracy by rounding.

So therefore, we can say that the solution to 𝑥 cubed plus five equals nine is 𝑥 is equal to the cube root of four.

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