Question Video: Solving a Cubic Equation by Expanding the Parentheses and Rearranging Mathematics • Second Year of Preparatory School

Video Transcript

Find the value of 𝑥 given that 15 minus three 𝑥 all cubed plus two is equal to 29.

In order to answer this question, we will first rearrange the equation so that the cubed term is isolated on the left-hand side. We do this by subtracting two from both sides, giving us 15 minus three 𝑥 all cubed is equal to 29 minus two. 29 minus two is equal to 27. And we can now take the cube roots of both sides of the equation. The cube root of 15 minus three 𝑥 all cubed is simply 15 minus three 𝑥. And since three cubed is 27, the cube root of 27 is equal to three. Our equation simplifies to 15 minus three 𝑥 is equal to three.

In order to solve for 𝑥, we can now subtract 15 from both sides so that negative three 𝑥 is equal to three minus 15. This in turn simplifies to negative three 𝑥 is equal to negative 12. And dividing through by three, we have 𝑥 is equal to four. The value of 𝑥 that satisfies the equation 15 minus three 𝑥 all cubed plus two is equal to 29 is four.