Question

If you're using the method of completing the square to solve the equation x² + 3x + 37 = 0, which number would have to be squared?

A) 3
B) 37
C) 3/2
D) None of the above

Answer 1

To solve the equation x² + 3x + 37 = 0 using the completing the square method, the number to be squared is 3/2, which is option C.

Step-by-step explanation:

When using the method of completing the square to solve the equation x² + 3x + 37 = 0, we are looking for a number that, when squared, will complete the perfect square trinomial of the quadratic equation.

In the given equation, we collect the x-terms on one side, leading to x² + 3x = -37. To complete the square, we need to add a number to both sides that is equal to (b/2)², where b is the coefficient of x. In this case, b = 3. Therefore, the number we need to square is b/2, and so (3/2)² is the correct answer.

Adding (3/2)², which is 2.25 or 9/4, to both sides of the equation will yield a perfect square trinomial on the left-hand side of the equation. Thus, you have the equation x² + 3x + (3/2)² = -37 + (3/2)², which simplifies to (x + 3/2)² = -37 + 9/4.