To solve the quadratic equation 2x²+12x-110=0 using the completing the square method, follow these steps:
1. Move the constant term to the other side of the equation: 2x²+12x=110.
2. Divide the entire equation by the coefficient of x² to make the coefficient 1: x²+6x=55.
3. Take half of the coefficient of x (6) and square it: (6/2)² = 9.
4. Add this value to both sides of the equation: x²+6x+9=55+9.
5. Simplify: (x+3)²=64.
6. Take the square root of both sides: √((x+3)²)=√64.
7. Solve for x: x+3=±8.
8. Subtract 3 from both sides: x=-3±8.
So the solutions to the equation 2x²+12x-110=0 are x=-3+8 and x=-3-8.