Solve the following in complete square method:2x^2+12x+3=0?

To solve the equation 2x^2 + 12x + 3 = 0 using the complete square method, we need to first make the coefficient of x^2 equal to 1 by dividing the entire equation by 2:

x^2 + 6x + 3/2 = 0

Next, we need to complete the square by adding and subtracting (b/2)^2 to the equation, where b is the coefficient of x:

x^2 + 6x + (6/2)^2 - (6/2)^2 + 3/2 = 0
x^2 + 6x + 9 - 9 + 3/2 = 0
(x + 3)^2 - 9/2 = 0

Now, we can rewrite the equation in the form of (x + a)^2 = b:

(x + 3)^2 = 9/2

Taking the square root of both sides:

x + 3 = ±√(9/2)
x + 3 = ±√(9)/√(2)
x + 3 = ±3/√(2)
x = -3 ± 3√2

Therefore, the solutions to the equation 2x^2 + 12x + 3 = 0 are x = -3 + 3√2 and x = -3 - 3√2.

Step 1: Move the constant term to the other side
2x^2 + 12x = -3

Step 2: Divide the equation by the coefficient of x^2
x^2 + 6x = -3/2

Step 3: Add the square of half the coefficient of x to both sides
x^2 + 6x + 9 = -3/2 + 9
(x + 3)^2 = 15/2

Step 4: Solve for x
x + 3 = ±√(15/2)
x = -3 ± √(15/2)

Therefore, the solutions are:
x = -3 + √(15/2) and x = -3 - √(15/2)

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