Question
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Solve the equation for all values of $\mathrm{x}$ by completing the square.
\[
x^{2}+18 x=-68
\]

Answer Attempt 1 out of 2
() Additional Solution $\Theta$ No Solution
\[
x=
\]
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Step 1 ：The given equation is a quadratic equation. To solve for x, we can use the method of completing the square. This involves rearranging the equation to the form \((x-a)^2 = b\), and then taking the square root of both sides.

Step 2 ：First, we need to move the constant term to the right side of the equation. So, the equation becomes \(x^{2}+18 x = -68\).

Step 3 ：Then, we need to complete the square on the left side by adding and subtracting the square of half the coefficient of x. This gives us \((x+9)^2 = 13\).

Step 4 ：Finally, we can solve for x by taking the square root of both sides. This gives us two solutions for the equation, which are \(-9 - \sqrt{13}\) and \(-9 + \sqrt{13}\). These are the two possible values of x that satisfy the equation.

Step 5 ：Final Answer: The solutions to the equation are \(\boxed{-9 - \sqrt{13}}\) and \(\boxed{-9 + \sqrt{13}}\).