Question

The model represents an equation. 1 1 -1 -1 000 000 AAA AA 1 -1 -1 What value of x makes the equation true?

1. x = 0
2. x = 1
3. x = -1
4. x = 2

Answer 1

The value of x that makes the equation true is approximately 0.0131.

Step-by-step explanation:

The quadratic equation representing the model is:

x² + 0.0211x - 0.0211 = 0

Using the quadratic formula, we can solve for x:

1. 
   
3. 
   

   Plug in the values of a, b, and c into the quadratic formula:

   
   

   x = (-b ± √(b² - 4ac)) / (2a)

   
   

   x = (-0.0211 ± √(0.0211² - 4(1)(-0.0211))) / (2(1))

   
   
4. 
   
6. 
   

   Simplify the expression under the square root:

   
   

   x = (-0.0211 ± √(0.00044421 + 0.08484)) / 0.0422

   
   

   x = (-0.0211 ± √0.08528421) / 0.0422

   
   

   x = (-0.0211 ± 0.2919) / 0.0422

   
   
7. 
   
9. 
   

   Calculate the two possible values of x:

   
   

   x = (-0.0211 + 0.2919) / 0.0422 ≈ 0.0131

   
   

   x = (-0.0211 - 0.2919) / 0.0422 ≈ -0.7085

   
   

Therefore, the value of x that makes the equation true is approximately 0.0131.