Question

If using the method of completing the square to solve the quadratic equation x² + 5x + 4 = 0, which number would have to be added to "complete the square"?​

Answer 1

To complete the square of the quadratic equation x² + 5x + 4 = 0, you need to add a number that is equal to half the coefficient of x squared (which is 1) squared, or (1/2)² = 1/4. Therefore, you need to add 1/4 to both sides of the equation as follows:

x² + 5x + 4 + 1/4 = 0 + 1/4

Next, simplify the left side of the equation by factoring the trinomial and combining like terms:

(x + 5/2)² = 1/4

Take the square root of both sides of the equation:

x + 5/2 = ±1/2

Solve for x by subtracting 5/2 from both sides of the equation:

x = -5/2 ± 1/2

Therefore, the solutions to the quadratic equation x² + 5x + 4 = 0, using the method of completing the square, are x = -5/2 + 1/2 and x = -5/2 - 1/2, or x = -2 and x = -3.

Answer 2

The number that would have to be added to "complete the square" is 4. This is because the equation can be rewritten as (x + 2.5)² = -4.5, and the number that needs to be added to both sides of the equation to make the left side a perfect square is 4.