Question

F(x)=4-3x-2x^2
I need answer solved by completing square with steps

Answer 1

After solving the equation f(x) = 4 - 3x - 2x^2 by completing the square, we get x = -3/4 ± √(3/4)^2 + 2.

Step-by-step explanation:

To solve f(x) = 4 - 3x - 2x^2 by completing the square, follow these steps:

1. Rearrange the equation to put the variable terms in order: -2x^2 - 3x + 4 = 0
2. Divide through by the coefficient of x^2 (in this case, -2) to make it 1: x^2 + (3/2)x - 2 = 0
3. Complete the square by adding the square of half the coefficient of x to both sides: x^2 + (3/2)x + (3/4)^2 - 2 + (3/4)^2 = (3/4)^2
4. Simplify and factor the perfect square trinomial: (x + 3/4)^2 = (3/4)^2 + 2
5. Take the square root of both sides to solve for x: x + 3/4 = ±√(3/4)^2 + 2
6. Finally, solve for x by subtracting 3/4 from both sides: x = -3/4 ± √(3/4)^2 + 2