Answer:
{-6.59, -9.41}
Step-by-step explanation:
I like this problem. In order to start solving by completing the square, you need to get the left side in this form: a^2 + bx. Everything else needs to go to the other side of the equation. So step 1, subtract 62 from both sides. And the equation should look like x^2 + 16x = -62.
Then for step 2 you need to add (b/2)^2 to both sides. b is the 16 in our equation. So (16/2)^2 equals 64. So add 64 to both sides. So the equation should look like x^2 + 16x + 64 = 2. Now, you have completed the square and just need to factor for step 3. Because we completed the square, x^2 + 16 x + 64 will factor into the form (x + (b/2))^2. So it'll look like (x+8)^2 = 2. This is where you can click which form it is on your computer. It's addition, and fill in the numbers from left to right as 8 and 2. Step 4 is taking the square root of both sides. The square root on the left side will just cancel the square and leave you with x + 8, and the square root 2 - I would wait to simplify, so just leave it as x + 8 =
[tex] \sqrt{2} [/tex]
For step 5, you need to isolate x by subtracting 8 from both sides. So now you should have x = [tex] \sqrt{2} [/tex]
- 8. Now to simplify for step 6. Now in the calculator, type "sqr rt btn" 2 (close any parentheses at this point) and type minus 8. This is one solution - -6.59. Then, because you have a positive and negative solution from a square root, type neg. "sqr rt btn" 2 close parentheses for square root and neg if applicable, and type minus 8. and you should get -9.41 as your other solution. Now to go back and check out solutions, plug in one solution to x into the calculator and solve it. If the final statement is true, then the solution is true. then do same thing for other solution. Make sure they are rounded to the nearest hundredth as the directions read.
