Question

Select all the equations that are equivalent to 81x² + 180x - 200 = 100

A. 81x² + 180x - 100 = 0
B. 81x² + 180x+100 = 200
C. 81x² + 180x + 100 = 400
D. (9x + 10)² = 400
E. (9x + 10)² = 0
F. (9x 10)² = 10
G. (9x - 10)² = 20

Answer 1

The only equation equivalent to the given quadratic equation 81x² + 180x - 200 = 100 is option D, which is (9x + 10)² = 400. Therefore, the correct answer is Option D.

Step-by-step explanation:

The question asks us to select equations that are equivalent to the given quadratic equation 81x² + 180x - 200 = 100. First, we need to simplify the given equation to identify its equivalent forms:

81x² + 180x - 200 = 100

81x² + 180x - 300 = 0 (Subtracting 100 from both sides)

Now, let's compare the simplified equation with the choices given:

• A. 81x² + 180x - 100 = 0 (Not equivalent, the constant term does not match)
• B. 81x² + 180x + 100 = 200 (Not equivalent, while adding 100 to both sides we should get 300 instead of 200)
• C. 81x² + 180x + 100 = 400 (Not equivalent, incorrect constant on both sides)
• D. (9x + 10)² = 400 (Equivalent, because expanding it we get 81x² + 180x + 100 = 400 and subtracting 100 from both sides gives the simplified equation)
• E. (9x + 10)² = 0 (Not equivalent, this would imply 9x + 10 = 0)
• F. (9x + 10)² = 10 (Not equivalent, incorrect constant on the right side)
• G. (9x - 10)² = 20 (Not equivalent, as when expanded it does not yield the simplified equation 81x² + 180x - 300 = 0)

So, the only equivalent equation to the original one is option D.