Solve the equation. Leave answer in simplest radical form.

n^2-2n+1=5

n^2-2n-4=0

a=1 b=-2 c=-4

then use quadratic formula
x=(-b+sqrt(b^2-4ac))/(2a)
x=(-b-sqrt(b^2-4ac))/(2a)

x=1+sqrt(5)
x=1-sqrt(5)

To solve the equation n^2 - 2n + 1 = 5, we first want to rearrange the equation to isolate the variable n on one side.

Move the constant term 5 to the other side:

n^2 - 2n + 1 - 5 = 0

Simplifying:

n^2 - 2n - 4 = 0

Next, we can use the quadratic formula to find the values of n that satisfy the equation.

The quadratic formula is given by:

n = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -2, and c = -4.

Plugging the values into the quadratic formula:

n = (-(-2) ± √((-2)^2 - 4(1)(-4))) / (2(1))

Simplifying further:

n = (2 ± √(4 + 16)) / 2
n = (2 ± √20) / 2
n = (2 ± 2√5) / 2

We can simplify this expression further by factoring out a common factor of 2:

n = 2(1 ± √5) / 2

Now, canceling out the common factor of 2 in the numerator and denominator:

n = 1 ± √5

Therefore, the solution to the equation n^2 - 2n + 1 = 5 in simplest radical form is:

n = 1 ± √5

To solve the equation n^2 - 2n + 1 = 5, we can start by isolating the variable on one side of the equation. Here's how:

Step 1: Subtract 5 from both sides of the equation:
n^2 - 2n + 1 - 5 = 5 - 5
n^2 - 2n - 4 = 0

Step 2: Now we have a quadratic equation in standard form (ax^2 + bx + c = 0), where a = 1, b = -2, and c = -4. We can solve it by factoring or using the quadratic formula.

Step 3: Let's try factoring. In this case, we need to find two numbers that multiply to ac (a * c) and add up to b. In our equation, ac = 1 * -4 = -4, and b = -2. So, the two numbers we're looking for are -4 and 1.

Step 4: Rewrite the equation using the two numbers we found:
n^2 - 4n + 3n - 4 = 0

Step 5: Group the terms and factor by grouping:
(n^2 - 4n) + (3n - 4) = 0
n(n - 4) + 3(n - 4) = 0
(n + 3)(n - 4) = 0

Step 6: Set each factor equal to zero and solve for n:
n + 3 = 0 or n - 4 = 0

For n + 3 = 0:
n = -3

For n - 4 = 0:
n = 4

Therefore, the solutions to the equation n^2 - 2n + 1 = 5 are n = -3 and n = 4.