Question

What number must you add to complete the square in the equation ( x² + 6x = 13 )?

A) ( (x+3)² = 22 )
B) ( (x+3)² = 4 )
C) ( (x+9)² = 22 )
D) ( (x+9)² = 4 )

Answer 1

To complete the square in the equation x² + 6x = 13, you need to add 9 to both sides of the equation. This simplifies the equation to (x+3)² = 22.

Step-by-step explanation:

To complete the square in the equation x² + 6x = 13, we need to add a constant term to both sides of the equation. To determine the constant term, we take half of the coefficient of the x term (which is 6) and square it. Half of 6 is 3, and 3 squared is 9. Therefore, we need to add 9 to both sides of the equation.

Adding 9 to both sides of the equation gives us (x² + 6x + 9 = 13 + 9), which simplifies to (x+3)² = 22.

Therefore, the correct option is A) ( (x+3)² = 22 ).