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8 February, 16:14

Complete the square x^2-10=16

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  1. 8 February, 16:37
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    (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
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