Solve the equation by the method of your choice. Simplify solutions, if possible.?

Question

2(x-1)^2 - 3= 47

It's not x=27 unfortunately. Is it {4, -6} ?

Answer 1

2(x-1)^2-3=47
2(x-1)^2 = 50
(x-1)^2 = 25
square root((x-1)^2) = square root(25)
x-1 = 5
x = 6

Answer 2

2(x-1)^2 - 3= 47 (transfer all knowns on one side, unknowns to the other)
2(x-1)^2 = 47+3
2(x-1)^2 = 50 /:2
(x-1)^2 = 25 (I see a potential for the difference of squares here, ie. x^2-y^2 = (x-y)(x+y), which will give us the solutions without meddling with the quadratic equation and roots)
(x-1)^2 - 25 = 0
(x-1)^2 - 5^2 = 0
(x-1-5)(x-1+5) = 0
(x-6)(x+4) = 0

x-6 = 0
x = 6
plug this in the equation, for checking:
2(x-1)^2 - 3= 47
2(6-1)^2 - 3 = 47
2*5^2 - 3 = 47
2*25 - 3 = 47
50-3 = 47
47 = 47 OK!

x+4 = 0
x = -4
check:
2(-4-1)^2 - 3= 47
2*(-5)^2 - 3 = 47
2*25 - 3 = 47
50-3 = 47
47 = 47 OK!

The solution is {-4, 6}

Answer 3

One thing you can do is expand everything out and solve for x using factoring or the quadratic formula. However, why? We have a square value right there, and we can easily solve for x without such methods.

What we're going to do is isolate the (x - 1)^2 and then take the square root of both sides.

2(x - 1)^2 - 3 = 47

Bring the -3 over to the right hand side, to get

2(x - 1)^2 = 50

And then divide both sides by 2, to get

(x - 1)^2 = 25

Now, take the square root of both sides. Keep in mind that whenever you take the square root of both sides in an equation, you have to add a "plus or minus" on the right hand side, or +/-.

x - 1 = +/- sqrt(25)

But we know what sqrt(25) is; it's 5.

x - 1 = +/- 5
Therefore
x = 1 +/- 5

So x = 1 + 5 or 1 - 5
x = {6, -4}

Answer 4

2(x-1)^2-3=47
2(x-1)^2=50
(x-1)^2=25
x-1=sqrt25
x-1=+or- 5

**NOTE: +or-5 as (-5)^2=25 and 5^5=25 **

x=+or-5+1

If -5 then x = -4,
If +5 then x = 6

With your answer of (-4,6), you have the negative signs the other way around.

Also the 2nd way would be multiplying out the brackets at (x-1)^2=25 and then factorising the quadratic, which will take slightly longer but will produce the same result

Answer 5

(x-1)^2 = x^2 - 2x + 1 so putting this into the equation

2x^2 - 4x + 2 -3 = 47

2x^2 -4x -48 = 0

factorising

(2x + 8)(x-6) =0

therefore x = 4 0r x = -6

Answer 6

2(x - 1)(x - 1) - 3 = 47
2(x^2 - x - x + 1) - 3 = 47
2(x^2 - 2x + 1) - 3 = 47
2x^2 - 4x + 2 - 3 - 47 = 0
2x^2 - 4x - 48 = 0
2(x^2 - 2x - 24) = 0
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x = 6
and x = -4

Answer 7

x=27

Answer 8

let's not forget the negative root.

it's -4 and 6

Answer 9

2(x^2-2x+2)-3=47

2x^2 - 4x + 4 - 3 = 47

2x^2 - 4x + 1 = 47

2x^2 - 4x - 46 = 0

x = 5.899 or x = -3.899

Answer 10

2(X-1)^2 - 3 = 47
2(X-1)^2 = 50
(X-1)^2=25
X-1=5
X=6