Complete the square x^2-10=16

(x - 5) ² = 41

Step-by-step explanation:

* Lets revise the completing square form

- the form x² ± bx + c is a completing square if it can be put in the form

(x ± h) ², where b = 2h and c = h²

# The completing square is x² ± bx + c = (x ± h) ²

# Remember c must be positive because it is = h²

* Lets use this form to solve the problem

∵ x² - 10x = 16

- Lets equate 2h by - 10

∵ 2h = - 10 ⇒ divide both sides by 2

∴ h = - 5

∴ h² = (-5) ² = 25

∵ c = h²

∴ c = 25

- The completing square is x² - 10x + 25

∵ The equation is x² - 10x = 16

- We will add 25 and subtract 25 to the equation to make the

completing square without change the terms of the equation

∴ x² - 10x + 25 - 25 = 16

∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides

∴ (x² - 10x + 25) = 41

* Use the rule of the completing square above

- Let (x² - 10x + 25) = (x - 5) ²

∴ (x - 5) ² = 41