If (x - 2)^2 = 49, then x could be
(A) -9
(B) -7
(C) 2
(D) 5
(E) 9
(x - 2)^2 = 49
(x - 2) (x - 2) = 49
x^2 - 2x - 2x + 4 = 49
x^2 - 4x + 4 - 4 = 49 - 4
x^2 - 4x = 45
I am not sure what to do from here.
why not just take the √ of both sides as it stands
(x-2)^2 = 49
x-2 = ± 7
x = 2 ± 7
= 9 or -5
you had x^2 - 4x - 45 = 0
which would have factored to
(x-9)(x+5) = 0
x = 0 or x = -5
I'm sorry I figured out what I did wrong.
(x - 2)^2 = 49
(x - 2) (x - 2) = 49
x^2 - 2x - 2x + 4 = 49
x^2 - 4x + 4 = 49
x^2 - 4x + 4 - 49 = 49 - 49
x^2 - 4x - 45 = 0
(x + 5) (x - 9) = 0
Solution is {-5} , {9}, Answer choice E
To continue solving the equation, you can use the quadratic formula or factorization.
Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we have x^2 - 4x = 45, which is equivalent to x^2 - 4x - 45 = 0.
Comparing this to the quadratic formula, we have:
a = 1, b = -4, and c = -45.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-45))) / (2(1))
x = (4 ± √(16 + 180)) / 2
x = (4 ± √196) / 2
x = (4 ± 14) / 2
Simplifying further, we have two possible solutions:
x = (4 + 14) / 2 = 18 / 2 = 9
x = (4 - 14) / 2 = -10 / 2 = -5
Therefore, x could be 9 or -5.
Out of the given answer choices, x can indeed be 9, so the correct answer is (E) 9.