Solving the quadratic equation 2x² - 7x + 3 = 0 using the completing the square method.

Final Answer:
x = 3 or x = 0.5

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Explanation:
Let’s solve this step by step, like we’re building a puzzle.

Step 1: We have 2x² – 7x + 3 = 0.
The “2” in front of x² is annoying because completing the square works best when it’s just x². So let’s divide everything by 2 to make it easier:

x² – (7/2)x + 3/2 = 0

Step 2: Move the number without x to the other side:

x² – (7/2)x = –3/2

Step 3: To complete the square, take half of the middle number (which is –7/2), then square it.

Half of –7/2 is –7/4.
Now square it: (–7/4)² = 49/16

Step 4: Add that number to both sides:

x² – (7/2)x + 49/16 = –3/2 + 49/16

Step 5: Left side becomes a perfect square:

(x – 7/4)² = –24/16 + 49/16 = 25/16

Step 6: Take square root of both sides:

x – 7/4 = ±5/4

Step 7: Solve for x:

x = 7/4 + 5/4 → x = 12/4 = 3
x = 7/4 – 5/4 → x = 2/4 = 0.5

So the two answers are x = 3 and x = 0.5.

You can check them by plugging back into the original equation — they work!