A) First, use the "completing the square" process to write this equation in the form (x+D)^2=E and enter your results below.

x^2-2x-24=0 is equivalent to:

Preview left side of eqn:

B) Solve your equation and enter your answers below as a list of numbers, separated with a comma where necessary.

1 answer

A) To complete the square, we need to add and subtract a constant value to the equation based on the coefficient of x.

The coefficient of x is -2, so we need to add and subtract (2/2)^2 = 1 to the equation.

x^2 - 2x - 24 + 1 - 1 = 0
(x^2 - 2x + 1) - 25 = 0
(x - 1)^2 - 25 = 0

The equation x^2 - 2x - 24 = 0 is equivalent to (x - 1)^2 - 25 = 0.

B) To solve the equation, we set it equal to zero and isolate the squared term:

(x - 1)^2 - 25 = 0
(x - 1)^2 = 25

Taking the square root of both sides:

x - 1 = ± √25
x - 1 = ± 5

Solving for x:

x = 1 + 5 = 6
x = 1 - 5 = -4

The solutions to the equation x^2 - 2x - 24 = 0 are x = 6 and x = -4.