Solve the quadratic equation 0=2x 2 +8x−4.

The given quadratic equation is 0 = 2x^2 + 8x - 4.

Step 1: Simplify the equation We can simplify the equation by dividing all terms by 2, which gives us: 0 = x^2 + 4x - 2

Step 2: Use the quadratic formula The quadratic formula is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this equation, a = 1, b = 4, and c = -2.

Step 3: Substitute the values of a, b, and c into the formula This gives us x = [-4 ± sqrt((4)^2 - 41(-2))] / (2*1) Simplify under the square root to get x = [-4 ± sqrt(16 + 8)] / 2 Further simplification gives x = [-4 ± sqrt(24)] / 2

Step 4: Simplify the square root The square root of 24 can be simplified to 2sqrt(6), so the equation becomes x = [-4 ± 2sqrt(6)] / 2

Step 5: Simplify the equation This gives us the final solutions: x = -2 ± sqrt(6)

So, the solutions to the equation 0 = 2x^2 + 8x - 4 are x = -2 + sqrt(6) and x = -2 - sqrt(6).