Following completion of your weekly readings, complete Projects #1 and 2 at the end of Chapter 7 in your textbook, Mathematics in Our World. 4x² - 4x +3=0?

Your equation has complex solutions. They can be found by "completing the square" or by using the quadratic formula.
4x^2 - 4x + 3 = 0
4x^2 - 4x = -3    (removing the constant from the left side can make it easier to see how to complete the square)
4x^2 - 4x + 1 = -2    (add (b^2)/(4a) to make ax^2 + bx into a perfect square)
(2x - 1)^2 = -2    (rewrite as a square)
2x - 1 = ±√(-2) = ±I√2    (take the square root of both sides)
2x = 1 ± I√2    (add 1)
x = (1 ± I√2)/2    (divide by 2)
thanked the writer.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://education.blurtit.com/3204133/following-completion-of-your-weekly-readings-complete-projects-1-and-2-at-the-end-of", "fetch_time": 1638219795000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2021-49/segments/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00059.warc.gz", "warc_record_offset": 305040068, "warc_record_length": 11451, "token_count": 235, "char_count": 665, "score": 4.0625, "int_score": 4, "crawl": "CC-MAIN-2021-49", "snapshot_type": "latest", "language": "en", "language_score": 0.8861398696899414, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00039-of-00064.parquet"}