What is the value of x in the equation 2x^2 - 8x + 6 = 0?

What is the value of x in the equation 2x^2 - 8x + 6 = 0?

Step 1: Identify the equation you need to solve: 2x^2 - 8x + 6 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c = 0, where a = 2, b = -8, and c = 6.
Step 3: Use the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).
Step 4: Calculate b^2 - 4ac: First, find b^2 = (-8)^2 = 64. Then calculate 4ac = 4 * 2 * 6 = 48. Now, subtract: 64 - 48 = 16.
Step 5: Substitute the values into the quadratic formula: x = [8 ± sqrt(16)] / (2 * 2).
Step 6: Calculate sqrt(16) = 4. Now the equation is: x = [8 ± 4] / 4.
Step 7: Solve for the two possible values of x: First, x = (8 + 4) / 4 = 12 / 4 = 3. Second, x = (8 - 4) / 4 = 4 / 4 = 1.
Step 8: Conclude that the values of x are 3 and 1.

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