Solve for x in the following equation.

Question

asked Sep 28, 2020 85.4k views

2 Answers

Steve Cobb · Answer 1 · 2020-10-05T01:57:50+0000

Answer: Option B

x_1 = 2 and
x_2 = 8

Explanation:

We have the equation
x ^ 2 -10x +16 = 0 and we want to solve for x.

To solve we can factor the expression and write it as the product of 2 factors.

To do this we must look for 2 numbers h and k such that adding h + k results in -10, and multiplying h*k results in 16.

Then the expression will have the form:

x ^ 2 -10x +16 = (x+h)(x+k) = 0

You can verify that these numbers are:

$h = -8\\k = -2$

Then we have to:

x ^ 2 -10x +16 = (x-8)(x-2) = 0

Then the solutions are:

x_1 = 2 and
x_2 = 8