Solve the equation and write the answer in simplified radical form.
n^2 - 2n + 1 = 5
(n-1)^2 = 5
n-1 = ±√5
n = 1±√5
n^2 - 2 n - 4 = 0
n = [ 2 +/- sqrt(4 + 16) ] / 2
n = [ 2 +/- 2 sqrt 5 ]/2
n = 1 +/- sqrt 5
To solve the equation n^2 - 2n + 1 = 5 and simplify the answer in radical form, follow these steps:
Step 1: Move all terms to one side of the equation.
n^2 - 2n + 1 - 5 = 0
Step 2: Simplify the equation.
n^2 - 2n - 4 = 0
Step 3: Use the quadratic formula to solve for n. The quadratic formula is given by:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -2, and c = -4. Substituting these values into the formula, we have:
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
Step 4: Simplify the expression.
n = 1 ± √5
Therefore, the solution to the equation n^2 - 2n + 1 = 5 in simplified radical form is n = 1 ± √5.