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.
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.
A) To complete the square for the equation x^2 - 2x - 24 = 0, follow these steps:
1. Move the constant term to the other side of the equation:
x^2 - 2x = 24
2. Take half of the coefficient of x (-2 in this case) and square it:
(-2/2)^2 = 1
3. Add the result from step 2 to both sides of the equation:
x^2 - 2x + 1 = 24 + 1
4. Simplify both sides of the equation:
x^2 - 2x + 1 = 25
5. Rewrite the left side of the equation as a perfect square:
(x - 1)^2 = 25
B) To solve the equation (x - 1)^2 = 25, follow these steps:
1. Take the square root of both sides of the equation:
sqrt((x - 1)^2) = sqrt(25)
2. Remove the square root on the left side:
x - 1 = ±5
3. Solve for x by adding 1 to both sides of the equation:
x = 1 ± 5
The solutions to the equation x^2 - 2x - 24 = 0 are x = 1 + 5 and x = 1 - 5, which can be simplified as x = 6 and x = -4, respectively.