Question

completing the square to solve a quadratic equation when a ≠ 1 solve 2x² + x - 4 = 0 x² + \boxed{}x + \boxed{} = 0

Explanation:

Step1: Divide all terms by 2

Divide each term in $2x^2 + x - 4 = 0$ by 2 to make the coefficient of $x^2$ equal to 1.
$\frac{2x^2}{2} + \frac{x}{2} - \frac{4}{2} = \frac{0}{2}$
Simplifies to: $x^2 + \frac{1}{2}x - 2 = 0$

Step2: Rearrange constant to right side

Move the constant term to the right side of the equation to prepare for completing the square.
$x^2 + \frac{1}{2}x = 2$
(To match the given blank format $x^2 + \square x + \square = 0$, rewrite the equation by moving 2 back to the left: $x^2 + \frac{1}{2}x + (-2) = 0$)

Answer:

The first blank is $\frac{1}{2}$ and the second blank is $-2$