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Solve by completing the square.\newlined2−28d=11d^2 - 28d = 11\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____

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Q. Solve by completing the square.\newlined2−28d=11d^2 - 28d = 11\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____
  1. Write Equation Form: Write the equation in the form of d2+bd=cd^2 + bd = c. The given equation is already in this form: d2−28d=11d^2 - 28d = 11.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineAdd 28d28d to both sides to isolate the d2d^2 term.\newline$d^\(2\) - \(28\)d + \left(\frac{\(28\)}{\(2\)}\right)^\(2\) = \(11\) + \left(\frac{\(28\)}{\(2\)}\right)^\(2\)
  3. Complete the Square: Complete the square by adding \((\frac{28}{2})^2\) to both sides.\(\newline\)\((\frac{28}{2})^2 = 196\), so we add \(196\) to both sides.\(\newline\)\(d^2 − 28d + 196 = 11 + 196\)\(\newline\)\(d^2 − 28d + 196 = 207\)
  4. Factor Left Side: Factor the left side of the equation.\(\newline\)The left side is a perfect square trinomial.\(\newline\)\((d - 14)^2 = 207\)
  5. Take Square Root: Take the square root of both sides of the equation.\(\newline\)\(\sqrt{(d − 14)^2} = \pm\sqrt{207}\)\(\newline\)\(d − 14 = \pm\sqrt{207}\)
  6. Solve for d: Solve for d by adding \(14\) to both sides.\(\newline\)\(d = 14 \pm \sqrt{207}\)
  7. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary.\(\newline\)\(\sqrt{207} \approx 14.39\)\(\newline\)\(d \approx 14 \pm 14.39\)
  8. Find Values of \(\newline\)\(d\): Find the two values of \(\newline\)\(d\).\(\newline\)\(\newline\)\(d \approx 14 + 14.39\) implies \(\newline\)\(d \approx 28.39\).\(\newline\)\(\newline\)\(d \approx 14 - 14.39\) implies \(\newline\)\(d \approx -0.39\).\(\newline\)Values of \(\newline\)\(d\): \(\newline\)\(28.39, -0.39\)

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