What is the solution to the equation 4x^2 - 12x + 9 = 0?

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Question: What is the solution to the equation 4x^2 - 12x + 9 = 0?

Options:

Correct Answer: x = 3

Solution:

Factor the equation: (2x - 3)(2x - 3) = 0. Thus, x = 3.

What is the solution to the equation 4x^2 - 12x + 9 = 0?

What is the solution to the equation 4x^2 - 12x + 9 = 0?

Step 1: Start with the equation 4x^2 - 12x + 9 = 0.
Step 2: Identify the coefficients: a = 4, b = -12, c = 9.
Step 3: Look for two numbers that multiply to (a * c) = 4 * 9 = 36 and add to b = -12.
Step 4: The numbers -6 and -6 work because -6 * -6 = 36 and -6 + -6 = -12.
Step 5: Rewrite the equation using these numbers: 4x^2 - 6x - 6x + 9 = 0.
Step 6: Group the terms: (4x^2 - 6x) + (-6x + 9) = 0.
Step 7: Factor out common terms: 2x(2x - 3) - 3(2x - 3) = 0.
Step 8: Factor by grouping: (2x - 3)(2x - 3) = 0.
Step 9: Set each factor equal to zero: 2x - 3 = 0.
Step 10: Solve for x: 2x = 3, so x = 3/2.
Step 11: Since both factors are the same, the solution is x = 3/2.

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