Question

Rewrite the equation so that the left side is a factored perfect square.

3x2 ­ - 4x = 2

Answer 1

To rewrite the equation so that the left side is a factored perfect square, follow these steps:

Step-by-step explanation:

To rewrite the equation so that the left side is a factored perfect square, we can complete the square in x. Here are the steps:

1. Start with the equation: 3x^2 - 4x = 2

2. Move the constant term to the right side: 3x^2 - 4x - 2 = 0

3. Take half of the coefficient of x (-4/2 = -2) and square it to get 4. Add this value to both sides of the equation: 3x^2 - 4x + 4 - 2 = 4

4. Factor the perfect square on the left side: (√(3x)^2 - 2)^2 = 4

5. Simplify the equation: (√(3x) - 2)^2 = 4

So, the equation rewritten with the left side as a factored perfect square is: (√(3x) - 2)^2 = 4

Answer 2

3x2 ­ - 4x = 2
6-4x=2
-6. -6
-4x=-4
/-4. /-4
x=1