The given equation is 2x² + 20x + 44 = 0.
To solve this quadratic equation by completing the square, we want to manipulate the equation into the form (px + q)² = r.
Step 1: Make sure the equation is in the form ax² + bx+ c = 0
It is clear that this step is already done.
Step 2: If a ≠ 1 and a ≠ 0, divide each side by 'a'
So, we divide the entire equation by 2, we get x² + 10x + 22 = 0
Step 3: Rearrange the equation to the form x² + bx = -c
x² + 10x = -22
Step 4: Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
The number needed is (b/2)². Here, b = 10 so (b/2)² = (10/2)² = 25. We add 25 to both sides.
So, x² + 10x + 25 = -22 + 25, this gives (x + 5)² = 3.
Step 5: Square root both sides of the equation
Taking the square root of both sides results in x + 5 = ±√3.
Step 6: Solve for 'x'
We subtract 5 from both sides to isolate 'x' on one side of the equation. This gives us:
x = -5 + √3 and x = -5 - √3.
So, the solutions of the equation 2x² + 20x + 44 = 0 are x = -5 + √3 and x = -5 - √3.