Question

Does the equation x2−4x−4=136
have the same solutions as the equation (x−2)2 =144
?(1 point)
Responses

Yes, because the solutions to both equations are x=14
and x=−10

Yes, because the solutions to both equations are x is equal to 14 and x is equal to negative 10

Yes, because the solutions to both equations are x=−14
and x=10

Yes, because the solutions to both equations are x is equal to negative 14 and x is equal to 10

No, because the solutions to the first equation are x=−14
and x=10
, and the solutions to the second equation are x=14
and x=−10

No, because the solutions to the first equation are x is equal to negative 14 and x is equal to 10, and the solutions to the second equation are x is equal to 14 and x is equal to negative 10

No, because the solutions to the first equation are x=14
and x=−10
, and the solutions to the second equation are x=−14
and x=10

Answer 1

Yes — the equations are equivalent. From x^2 − 4x − 4 = 136 we get x^2 − 4x = 140, so (x − 2)^2 = 144. Thus x − 2 = ±12, giving x = 14 or x = −10.