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Solve by completing the square.\newlineu2−26u=23u^2 - 26u = 23\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____

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Q. Solve by completing the square.\newlineu2−26u=23u^2 - 26u = 23\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____
  1. Write equation in standard form: Write the equation in the form of u2+bu=cu^2 + bu = c. The given equation is already in this form: u2−26u=23u^2 - 26u = 23.
  2. Move constant term: Move the constant term to the right side of the equation.\newlineAdd 2323 to both sides to isolate the uu terms on one side.\newline$u^\(2\) - \(26\)u + \left(\frac{\(26\)}{\(2\)}\right)^\(2\) = \(23\) + \left(\frac{\(26\)}{\(2\)}\right)^\(2\)
  3. Complete the square: Complete the square by adding \((\frac{26}{2})^2\) to both sides.\(\newline\)\((\frac{26}{2})^2 = 169\), so add \(169\) to both sides.\(\newline\)\(u^2 − 26u + 169 = 23 + 169\)\(\newline\)\(u^2 − 26u + 169 = 192\)
  4. Factor left side: Factor the left side of the equation.\(\newline\)The left side is a perfect square trinomial.\(\newline\)\((u - 13)^2 = 192\)
  5. Take square root: Take the square root of both sides of the equation.\(\newline\)\(\sqrt{(u - 13)^2} = \pm\sqrt{192}\)\(\newline\)\(u - 13 = \pm\sqrt{192}\)
  6. Simplify square root: Simplify the square root of \(192\).\(\sqrt{192} = \sqrt{64\times3} = \sqrt{64} \times \sqrt{3} = 8\sqrt{3}\)\(u - 13 = \pm8\sqrt{3}\)
  7. Solve for u: Solve for u by adding \(13\) to both sides of the equation.\(\newline\)\(u = 13 \pm 8\sqrt{3}\)
  8. Approximate square root: Approximate the square root of \(3\) to the nearest hundredth and solve for \(u\).\(\sqrt{3} \approx 1.73\)\(u \approx 13 \pm 8 \times 1.73\)\(u \approx 13 \pm 13.84\)
  9. Find two values: Find the two values of \(u\).\(u \approx 13 + 13.84\)\(u \approx 26.84\)\(u \approx 13 - 13.84\)\(u \approx -0.84\)

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