Question

Solve the quadratic equation by completing the square. x^2-9x-22=0Completing the square gives us: (x- Answer )^2 = AnswerEnter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.x=Answer and x=Answer

Answer 1

Answer::

`\begin{gathered} (x-(9)/(2))^2=(169)/(4) \\ x=-2\text{ and x=11} \end{gathered}`

Step-by-step explanation:

Given the quadratic equation:

`x^2-9x-22=0`

To solve it by completing the square, follow the steps below:

Step 1: Take the constant to the right-hand side.

`x^2-9x=22`

Step 2: Divide the coefficient of x by 2, square it and add it to both sides.

`x^2-9x+(-(9)/(2))^2=22+(-(9)/(2))^2`

Step 3: Write the left-hand side as a perfect square.

`(x-(9)/(2))^2=(169)/(4)`

Step 4: Take the square root of both sides.

`\begin{gathered} \sqrt{(x-(9)/(2))^2}=\pm\sqrt{(169)/(4)} \\ x-(9)/(2)=\pm(13)/(2) \end{gathered}`

Step 5: Solve for x.

`\begin{gathered} x=(9)/(2)\pm(13)/(2)=(9\pm13)/(2) \\ \implies x=(9+13)/(2)\text{ or }x=(9-13)/(2)\text{ } \\ x=11\text{ or }x=-2 \end{gathered}`

So, we have:

`\begin{gathered} Completing\; the\; square\; gives\; us\colon(x-(9)/(2))^2=(169)/(4) \\ x=-2\text{ and x=11} \end{gathered}`