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For the quadratic equation x2+20x=69

𝑥
2
+
20
𝑥
=
69
, complete the table by testing each of the given values to determine whether it is a solution. Identify which one of these values is in the solution set.

(1 point)
Only x=
𝑥
=
is in the solution set.

3 answers

To determine whether a given value of x is a solution to the quadratic equation x2+20x=69, we can rearrange the equation as follows:

x2+20x−69=0

Now, let's test some values.

Here are the steps for testing a value of x:

  1. Substitute the value of x into the left side of the equation.
  2. Calculate the result.
  3. If the result equals zero, then that value is a solution.

Let's consider the following possible values for testing. Since no specific values were given, I'll demonstrate the process with a few arbitrary values, and you can substitute the specific values provided in your problem.

Testing Values

  1. Test x=−30: (−30)2+20(−30)−69=900−600−69=231(not a solution)

  2. Test x=−25: (−25)2+20(−25)−69=625−500−69=56(not a solution)

  3. Test x=−20: (−20)2+20(−20)−69=400−400−69=−69(not a solution)

  4. Test x=−15: (−15)2+20(−15)−69=225−300−69=−144(not a solution)

  5. Test x=−10: (−10)2+20(−10)−69=100−200−69=−169(not a solution)

  6. Test x=−5: (−5)2+20(−5)−69=25−100−69=−144(not a solution)

  7. Test x=0: 02+20(0)−69=0−69=−69(not a solution)

  8. Test x=3: 32+20(3)−69=9+60−69=0(this is a solution)

  9. Test x=5: 52+20(5)−69=25+100−69=56(not a solution)

  10. Test x=6: 62+20(6)−69=36+120−69=87(not a solution)

Conclusion

From our tests, x=3 satisfies the equation and is the only value in the solution set among the values we tested.

Therefore, only x=3 is in the solution set. You can replace x=3 with whatever specific values you have to check against the equation.

If you have specific values to check, please provide them, and I can assist further.

Answer

Only x=3 is in the solution set for the equation x2+20x=69.