Answer:
x = 3 or 7
Step-by-step explanation:
Solve by completing the square:
First, move the constants to one side:
Then, add to both sides to make the right a perfect square trinomial, which is easy to factor:
Simplify and Factor:
Finally, square root both sides using the even roots property:
x - 5 = ± 2
x = 5 ± 2
x = 3 or x = 7
A <em>difference of squares</em> is exactly what it suggests - the difference between two perfect squares. 25 - 9, 4 - 1, x² - 25, and 125 - b² are just a few examples. Differences of squares factor very nicely, too. For any difference of squares x² - y²:
x² - y² = (x + y)(x - y)
We can see that this is true by taking the right side of the equation and distributing:
(x + y)(x - y) = (x + y) · x + (x + y) · (-y) = x² + xy - xy - y² = x² - y²
We notice in our given expression that 36 is a perfect square - namely, 6². We want the expression x² + ?x - 36 to look like x² - 6², which we can accomplish if we replace the question mark with a 0.