Answer:
x=-2
Step-by-step explanation:
To complete the square for the quadratic equation \(2x^2 + 2x - 4 = 0\), follow these steps:
1. Start with the quadratic equation in the form \(ax^2 + bx + c = 0\).
\(2x^2 + 2x - 4 = 0\)
2. Divide the entire equation by the coefficient of \(x^2\) (in this case, 2) to make the coefficient of \(x^2\) equal to 1.
\(x^2 + x - 2 = 0\)
3. Move the constant term to the other side of the equation.
\(x^2 + x = 2\)
4. Add and subtract \((b/2)^2\) to complete the square. The coefficient of \(x\) is 1, so \(b/2\) is \((1/2)\). Square \((1/2)\) to get \(1/4\), and add and subtract it to the equation.
\(x^2 + x + \frac{1}{4} - \frac{1}{4} = 2\)
5. Factor the perfect square trinomial and simplify.
\((x + \frac{1}{2})^2 - \frac{9}{4} = 0\)
6. Move the constant term to the other side of the equation.
\((x + \frac{1}{2})^2 = \frac{9}{4}\)
7. Take the square root of both sides.
\(x + \frac{1}{2} = \pm \frac{3}{2}\)
8. Solve for \(x\).
\(x = -\frac{1}{2} + \frac{3}{2}\) or \(x = -\frac{1}{2} - \frac{3}{2}\)
\(x = 1\) or \(x = -2\)
Therefore, the solution set for the quadratic equation \(2x^2 + 2x - 4 = 0\) is \(x = 1\) and \(x = -2\).
