Math Summary

Question

I need to work out this problem

x² - 14x + 74 = 0

 

But in step by step but written in summary as if i'm the tutor teaching and telling them step by step example...

 suppose the problem was x(x+1)...then, a sample summary would be something like:

take the x and multiply it out to each term in parenthesis...first we have x times x which is x^2 and we add this to x times 1 which is x to get x^2+x as our answer.
 

 

Answer 1

I need to work out this problem
x^2 - 14x + 74 = 0

We're going to use a method called completing the square.
Begin by subtracting 74 from both sides of the equation.

x^2 - 14x + 74 - 74 = 0 - 74
x^2 - 14x = -74

Next, we divide the coefficient of x by the coefficient of x^2, then
take 1/2 of that, and square it. We add that result to both sides
of the equation.

14/1 = 14
14 * 1/2 = 7
7 * 7 = 49

x^2 - 14x + 49 = -74 + 49
x^2 - 14x + 49 = -25

We can factor the left side of the equation.
(x - 7)(x - 7) = -25

The right side is a negative number. For this
problem, it means there are no real roots, i.e., the
graph of this equation does not cross the x-axis.

There are imaginary roots, though. In order to obtain
the square root of a negative number, we introduce i, which
is the square root of -1. Using that, the answer to this problem
becomes x - 7 = ±5i.

Which means that x = 7 + 5i  and x = 7 - 5i.