Solve the equation by completing the square. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 $$ Determine the appropriate process for rearranging the equation before completing the square to obtain an equation of the form $$ (x+k)^{2}= $$ d. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or a simplified fraction.) A. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow x^{2}-\frac{5}{2} x=\frac{39}{16} \Rightarrow x^{2}-\frac{5}{2} x+\frac{25}{16}=\frac{39}{16}+\frac{25}{16} $$ B. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow x^{2}-\frac{5}{2} x=\frac{39}{16} \Rightarrow x^{2}-\frac{5}{2} x+\quad=\frac{39}{16} $$ C. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow \frac{2}{5} x^{2}-x=\frac{39}{40} \Rightarrow \frac{2}{5} x^{2}-x+=\frac{39}{40}+ $$ D. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow \frac{2}{5} x^{2}-x=\frac{39}{40} \Rightarrow \frac{2}{5} x^{2}-x+\quad=\frac{39}{40} $$ The solution set is $$ \left\{\begin{array}{l} ext { A. } \ ext { (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or simplified fractions for any } \ ext { numbers in the expression. Use a comma to separate answers as needed.) }\end{array} ight. $$ $$ \begin{array}{l} ext { a }\end{array} $$

Question

Solve the equation by completing the square. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 $$ Determine the appropriate process for rearranging the equation before completing the square to obtain an equation of the form $$ (x+k)^{2}= $$ d. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or a simplified fraction.) A. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow x^{2}-\frac{5}{2} x=\frac{39}{16} \Rightarrow x^{2}-\frac{5}{2} x+\frac{25}{16}=\frac{39}{16}+\frac{25}{16} $$ B. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow x^{2}-\frac{5}{2} x=\frac{39}{16} \Rightarrow x^{2}-\frac{5}{2} x+\quad=\frac{39}{16} $$ C. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow \frac{2}{5} x^{2}-x=\frac{39}{40} \Rightarrow \frac{2}{5} x^{2}-x+=\frac{39}{40}+ $$ D. $$ x^{2}-\frac{5}{2} x-\frac{39}{16}=0 \Rightarrow \frac{2}{5} x^{2}-x=\frac{39}{40} \Rightarrow \frac{2}{5} x^{2}-x+\quad=\frac{39}{40} $$ The solution set is $$ \left\{\begin{array}{l}	ext { A. } \ 	ext { (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or simplified fractions for any } \ 	ext { numbers in the expression. Use a comma to separate answers as needed.) }\end{array}ight. $$ $$ \begin{array}{l}	ext { a }\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ x^{2}-\frac{5}{2}x-\frac{39}{16}=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$x^{2}-\frac{5}{2}x-\frac{39}{16}=0$$
- step1: Factor the expression:
  $$\frac{1}{16}\left(4x-13ight)\left(4x+3ight)=0$$
- step2: Divide the terms:
  $$\left(4x-13ight)\left(4x+3ight)=0$$
- step3: Separate into possible cases:
  $$\begin{align}&4x-13=0\&4x+3=0\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=\frac{13}{4}\&x=-\frac{3}{4}\end{align}$$
- step5: Rewrite:
  $$x_{1}=-\frac{3}{4},x_{2}=\frac{13}{4}$$
The solutions to the equation $$x^{2}-\frac{5}{2}x-\frac{39}{16}=0$$ by completing the square are $$x_{1}=-\frac{3}{4}$$ and $$x_{2}=\frac{13}{4}$$.

Therefore, the correct process for rearranging the equation before completing the square is:

$$ x^{2}-\frac{5}{2}x-\frac{39}{16}=0 \Rightarrow x^{2}-\frac{5}{2}x=\frac{39}{16} \Rightarrow x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{39}{16}+\frac{25}{16} $$

This corresponds to option A.

The solution set is $$ \left\{-\frac{3}{4}, \frac{13}{4}ight\} $$.
The correct process is option A: $$ x^{2}-\frac{5}{2}x-\frac{39}{16}=0 \Rightarrow x^{2}-\frac{5}{2}x=\frac{39}{16} \Rightarrow x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{39}{16}+\frac{25}{16} $$ The solutions are $$ x = -\frac{3}{4} $$ and $$ x = \frac{13}{4} $$.

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