Understanding the Equation
The equation given is:
12 + 1 * 15 * 1 * 2 * 5 = + 4 * 5 * 3 * 1 * x * x - x - x
To determine which value of x (1, 2, 5, or 7) satisfies this equation, we will simplify both sides.
Left Side Calculation
- Start with the left side:
- 12 + 1 * 15 * 1 * 2 * 5
- Calculate the product first:
- 1 * 15 = 15
- 15 * 1 = 15
- 15 * 2 = 30
- 30 * 5 = 150
- Now add 12:
- 12 + 150 = 162
So, the left side equals 162.
Right Side Calculation
- Now simplify the right side:
- + 4 * 5 * 3 * 1 * x * x - x - x
- Calculate the product first:
- 4 * 5 = 20
- 20 * 3 = 60
- 60 * 1 = 60
- Now we have: 60 * x * x - 2x = 60x² - 2x
To find x, we set the left side equal to the right side:
- 162 = 60x² - 2x
Simplifying the Equation
Rearranging gives:
- 60x² - 2x - 162 = 0
Now, we can use the quadratic formula:
- x = [2 ± √(4 + 4 * 60 * 162)] / (2 * 60)
Calculating the discriminant:
- 4 + 4 * 60 * 162 = 38884
- √38884 ≈ 197.2
Now, substituting into the quadratic formula:
- x = [2 ± 197.2] / 120
Calculating both possible values for x gives approximately:
- x ≈ 1.66 or x ≈ -1.63
Since x must be a positive integer, we test the provided options.
Testing Options
- a) x = 1: 60(1)² - 2(1) = 58 (not equal to 162)
- b) x = 2: 60(2)² - 2(2) = 232 (not equal to 162)
- c) x = 5: 60(5)² - 2(5) = 1480 (not equal to 162)
- d) x = 7: 60(7)² - 2(7) = 2554 (not equal to 162)
Conclusion
None of the given options satisfy the equation as true.