Question 545970
<pre>
x² - 14x = -45

To find out what number to add to both sides,

1. Take the coefficient of x which is -14
2. Multiply it by {{{1/2}}} to get -14({{{-1/2}}}) = -7
3. Square that result:  (-7)² = 49
4. Add that number to both sides of the equation:

x² - 14x <font color = "red">+ 49</font> = -45 <font color = "red">+ 49</font>

Factor the left side, and combine the number on the right:

(x - 7)(x - 7) = 4

Write the left side as  (x - 7)²

      (x - 7)² = 4

Use the principle of square roots

         x - 7 = ±2

Use the +        Use the -

x - 7 = +2       x - 7 = -2
    x =  9           x = 5

 
Edwin</pre>