Explain how to solve 5x^2 - 3x = 25 by completing the square. What are the solutions?
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ᴘᴜᴛ ᴀʟʟ ᴛᴇʀᴍs ᴡɪᴛʜ ᴠᴀʀɪᴀʙʟᴇ ᴏɴ ᴏɴᴇ sɪᴅᴇ ᴀɴᴅ ᴛʜᴇ ᴄᴏɴsᴛᴀɴᴛs ᴏɴ ᴛʜᴇ ᴏᴛʜᴇʀ sɪᴅᴇ.
5x^2 - 3x = 252.
ғᴀᴄᴛᴏʀ ᴏᴜᴛ ᴛʜᴇ ᴄᴏᴇғғɪᴄɪᴇɴᴛ ᴏғ ᴛʜᴇ x^2 ᴛᴇʀᴍ
5(x^2 - 3x/5) = 253.
ɪɴsɪᴅᴇ ᴛʜᴇ ᴘᴀʀᴇɴᴛʜᴇsᴇs, ᴡᴇ ᴀᴅᴅ ᴀ ɴᴜᴍʙᴇʀ ᴛʜᴀᴛ ᴡᴏᴜʟᴅ ᴄᴏᴍᴘʟᴇᴛᴇ ᴛʜᴇ sǫᴜᴀʀᴇ ᴀɴᴅ ᴀʟsᴏ ᴀᴅᴅ ᴛʜɪs ᴛᴏ ᴛʜᴇ ᴏᴛʜᴇʀ sɪᴅᴇ ᴏғ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ.
In this case we add 9/100 and on the other side we add 9/20.5(x^2 - 3x/5 + 9/100) = 25 + 9/204.
We simplify as follows:
5(x^2 - 3x/5 + 9/100)
→25 + 9/205(x - 3/10)^2
→509/20(x - 3/10)^2
→ 509/100x1
→√(509) /100 + 3/10x2
→ -√(509) /100 + 3/10
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