Question

Number One)

Solutions please:
f(x)= (x−1)^2−36
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Number Two)
Harry solved a quadratic equation. His work is shown below.
In which step did Harry make an error?

Original: (x−5) ^2+6=42

Step One:(x−5)^2=36

Step Two: x-5=6

Step Three: x=11

Number Three:
(image)

Answer 1

Explanation:

(1)
`f(x) = (x-1)^(2) - 36`

First, let's expand the expression:

`f(x) = x^(2) -2x + 1 - 36`

`f(x) = x^(2) - 2x - 35`

Next, let's factor the quadratic:

`f(x) = (x - 7)(x + 5)`

Finally, set the equation equal to
`0` to find the solutions

`0 = (x - 7)(x + 5)`

`x = -5, 7`

(2) During the step
`(x - 5)^(2) = 36`, when you take the square root of both sides, you have two equations, rather than one:

`x - 5 = 6` and
`x - 5 = -6`, so the solutions should be
`x = -1, 11`

(3)

`(1)/(4)(x + 5)^(2) - 1 = 3`

Add
`1` to both sides

`(1)/(4)(x + 5)^(2) = 4`

Multiply both sides by
`4`

`(x + 5)^(2) = 16`

Take the square root of both sides

`x + 5 =`±
`4`

Subtract
`5` from both sides

`x = -9, -1`