Complete the square to solve the following quadratic equation: x2- 6x-20 = 20.
• x= 52, x = -46
• x= 10, x = -4
• x = -10, x = 4
• x=3+2√10, 3 - 21√10
To complete the square, we will first move the constant term to the right side of the equation:
x^2 - 6x - 20 = 20
x^2 - 6x - 40 = 0
Next, we need to take half of the coefficient of the x-term, square it, and add it to both sides of the equation. The coefficient of the x-term is -6, so:
(-6/2)^2 = 9
x^2 - 6x + 9 = 40 + 9
x^2 - 6x + 9 = 49
Now, we can factor the left side of the equation as a perfect square:
(x - 3)^2 = 49
Taking the square root of both sides:
x - 3 = ±7
Solving for x:
x = 3 + 7
x = 10
or
x = 3 - 7
x = -4
Therefore, the solutions to the quadratic equation are x = 10 and x = -4. The correct answer is x = 10, x = -4.