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Solve by completing the square.\newliner2−26r=11r^2 - 26r = 11\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve by completing the square.\newliner2−26r=11r^2 - 26r = 11\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Write Equation Form: Write the equation in the form of r2+br=cr^2 + br = c. The given equation is already in this form: r2−26r=11r^2 - 26r = 11.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineAdd 26r26r to both sides to isolate the r2r^2 term.\newline$r^\(2\) - \(26\)r + \left(\frac{\(26\)}{\(2\)}\right)^\(2\) = \(11\) + \left(\frac{\(26\)}{\(2\)}\right)^\(2\)
  3. Complete the Square: Complete the square by adding \((\frac{26}{2})^2\) to both sides of the equation.\(\newline\)\((\frac{26}{2})^2 = 169\), so we add \(169\) to both sides.\(\newline\)\(r^2 − 26r + 169 = 11 + 169\)\(\newline\)\(r^2 − 26r + 169 = 180\)
  4. Factor Left Side: Factor the left side of the equation.\(\newline\)The left side is a perfect square trinomial.\(\newline\)\((r - 13)^2 = 180\)
  5. Take Square Root: Take the square root of both sides of the equation.\(\newline\)\(\sqrt{(r - 13)^2} = \pm\sqrt{180}\)\(\newline\)\(r - 13 = \pm\sqrt{180}\)
  6. Simplify Square Root: Simplify the square root of \(180\).\(\sqrt{180} = \sqrt{(36\times5)} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5}\)\(r - 13 = \pm6\sqrt{5}\)
  7. Solve for r: Solve for r by adding \(13\) to both sides of the equation. \(r = 13 \pm 6\sqrt{5}\)
  8. Approximate Values: Approximate the values of \(r\) to the nearest hundredth.\(6\sqrt{5} \approx 6 \times 2.236 = 13.416\)\(r \approx 13 \pm 13.416\)\(r \approx 26.416\) or \(r \approx -0.416\)

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