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Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______

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Solve a quadratic equation by completing the squareright chevron icon

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Q. Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______
  1. Rewrite equation in u2+bu=cu^2 + bu = c form: Rewrite the equation in the form of u2+bu=cu^2 + bu = c. Add 2323 to both sides to set the equation up for completing the square. u2−24u−23+23=0+23u^2 - 24u - 23 + 23 = 0 + 23 u2−24u=23u^2 - 24u = 23
  2. Add 2323 to both sides: Find the number to add to both sides to complete the square.\newlineSince (−24/2)2=144(-24/2)^2 = 144, add 144144 to both sides.\newlineu2−24u+144=23+144u^2 − 24u + 144 = 23 + 144\newlineu2−24u+144=167u^2 − 24u + 144 = 167
  3. Find number to complete the square: Factor the left side of the equation.\newlineu2−24u+144=167u^2 - 24u + 144 = 167\newline(u−12)2=167(u - 12)^2 = 167
  4. Factor the left side: Take the square root of both sides of the equation.\newline(u−12)2=167\sqrt{(u - 12)^2} = \sqrt{167}\newlineu−12=±167u - 12 = \pm\sqrt{167}
  5. Take square root of both sides: Solve for uu by adding 1212 to both sides.\newlineu−12+12=±167+12u - 12 + 12 = \pm\sqrt{167} + 12\newlineu=12±167u = 12 \pm \sqrt{167}
  6. Solve for uu by adding 1212: Calculate the approximate decimal values of uu.
    u≈12+167u \approx 12 + \sqrt{167} and u≈12−167u \approx 12 - \sqrt{167}
    u≈12+12.92u \approx 12 + 12.92 and u≈12−12.92u \approx 12 - 12.92
    u≈24.92u \approx 24.92 and u≈−0.92u \approx -0.92

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