Question

Find one value of x that is a solution to the equation: (2x - 3)² = 4x - 6.

a) 1
b) 2
c) 3
d) 4

Answer 1

To find a value of x that is a solution to the equation (2x - 3)² = 4x - 6, expand the equation, rearrange it, and solve the resulting quadratic equation by factoring, completing the square, or using the quadratic formula.

Step-by-step explanation:

To find a value of x that is a solution to the equation (2x - 3)² = 4x - 6, we can solve the equation by expanding the square, equating it to the right-hand side, and solving for x.

1. Expand the left-hand side: (2x - 3)² = 4x² - 12x + 9
2. Set the expanded equation to the right-hand side: 4x² - 12x + 9 = 4x - 6
3. Rearrange the equation: 4x² - 16x + 15 = 0
4. Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. The factored form of the equation is (2x - 3)(2x - 5) = 0, which gives us two possible values of x: x = 3/2 or x = 5/2.

Therefore, the correct answer is

a) 1

as none of the given options match the solutions to the equation.