Solve by completing the square.
x^2 + 22x − 3 = 0
To solve by completing the square, we want to rearrange the equation so that it is in the form (x + p)^2 = q.
First, add 3 to both sides of the equation:
x^2 + 22x = 3
Next, to complete the square, take half of the coefficient of x (in this case, half of 22) which is 11, square it, and add it to both sides of the equation:
x^2 + 22x + 121 = 3 + 121
(x + 11)^2 = 124
Now the equation is in the desired form, so we can solve for x:
x + 11 = ±√124
x = -11 ± √124
Therefore, the solutions are:
x = -11 + √124 or x = -11 - √124.