Solve the following quadratic equation by completing the square. If your solution has a radical then keep this in your answer and do not convert to a decimal.
x2−2x−35=0
(1 point)
Responses
x=1±35−−√
x is equal to 1 plus or minus square root of 35
x=±6
x is equal to plus or minus 6
x=5 and x=-7
x=5 and x=-7
x=7 and x=-5
To complete the square for the equation x^2 - 2x - 35 = 0, we first move the constant term to the right side:
x^2 - 2x = 35
Next, we need to find the value that will complete the square. The value is calculated by taking half of the coefficient of x (which is -2 in our case) and squaring it:
(-2/2)^2 = (-1)^2 = 1
Now we add and subtract this value inside the parentheses:
x^2 - 2x + 1 = 35 + 1
(x - 1)^2 = 36
Taking the square root of both sides:
x - 1 = ±6
x = 1 ± 6
Therefore, the solutions to the quadratic equation x^2 - 2x - 35 = 0, after completing the square, are:
x = 1 + 6
x = 7
x = 1 - 6
x = -5
So, the correct response is x = 7 and x = -5