Solve the equation for all values of x by completing the square.

Question

x, squared, plus, 4, x, equals, minus, 3
x
2
+4x=
−3

Answer 1

To complete the square, we need to add and subtract (4/2)^2 = 4 to both sides of the equation:

x^2 + 4x = -3
x^2 + 4x + 4 = -3 + 4
(x + 2)^2 = 1

Now, take the square root of both sides to solve for x:

x + 2 = ±1
x = -2 ± 1

Therefore, the solutions are x = -1 or x = -3.