Answer: To solve for all values of x in the equation x^2 - 2x - 48 = 0 by completing the square, we can follow these steps:
Bring the x term to one side of the equation by adding 2x to both sides: x^2 - 2x = 48
Divide the coefficient of the x^2 term (which is 1) by 2 and square it to find the value to add to both sides of the equation to complete the square: (1/2)^2 = 1/4. Add 1/4 to both sides of the equation: x^2 - 2x + 1/4 = 48 + 1/4
Take the square root of both sides of the equation: (x - 1)^2 = 192 + 1
Solve for x by taking the square root of both sides of the equation: x - 1 = ± √193
Add 1 to both sides of the equation to find the values of x: x = 1 ± √193
So the solutions of the equation are x = 1 + √193 and x = 1 - √193
It is important to notice that these are the solutions in radical form, so they are not exact values of x.
Explanation: