Question

Solve by completing the square
x² + 10x =-21

2x² + 16x + 42 = 0

Answer 1

x² + 10x =-21

To complete the square, we need to add and subtract (10/2)² = 25 on both sides of the equation:

x² + 10x + 25 = -21 + 25
(x + 5)² = 4

Now take the square root of both sides:

x + 5 = ±√4
x + 5 = ±2
x = -5 ± 2
x = -7 or x = -3

Therefore, the solutions are x = -7 or x = -3.


2x² + 16x + 42 = 0

First, divide the entire equation by 2 to simplify:

x² + 8x + 21 = 0

To complete the square, we need to add and subtract (8/2)² = 16 on both sides of the equation:

x² + 8x + 16 = -21 + 16
(x + 4)² = -5

There are no real solutions to this equation, as taking the square root of a negative number results in imaginary numbers.