Cubic Formula Proof Step 5: Putting it All Together to Solve for x

In this video I go over the fifth and final step of the Cubic Formula proof which involves putting all of the previous steps together to solve for the 3 solutions of x. The first solution of x is obtained by plugging in the first solution of y into the x-y substitution and replacing the p, q values with the a, b, c values. The second solution is obtained by simply copying the first solution and multiplying it by the corresponding complex conjugates from the cube root of unity. The third and final solution is obtained by copying the second solution and simply changing the signs of the complex conjugates. Because I used the copy and paste method in Microsoft OneNote, I may be the first person to show the complete solution being derived in real-time!

Timestamps

• Step 5: Plugging the y values into the x equation and replacing the p, q values: 0:00
• First solution for x: 2:20
• Second solution for x by copying the first solution and multiplying by complex conjugates: 8:20
• Third solution by copying the second solution and changing the signs of the complex conjugates: 11:32
• Double checking our solutions with the Hive account@blackpenredpen solutions: 12:03

Notes and playlists

• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EF05ExjzLbB64NgUjoV1hl
• Notes: @mes/dzekfnxh .

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