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29 March, 07:05

Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?

O 12 + V11,2 - V11)

01-2 + V11.-2 - V11]

012+.15.2+7)

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  1. 29 March, 07:30
    0
    x = 2 + √11 or x = 2 - √11

    Step-by-step explanation:

    I am going to complete the square step-by-step.

    x² - 4x - 7=0

    Step 1: Add 7 to both sides.

    x² - 4x - 7 + 7 = 0 + 7

    x² - 4x = 7

    Step 2: The coefficient of - 4x is - 4. Let b = - 4.

    Then we need to add (b/2) ² = 4 to both sides to complete the square.

    Add 4 to both sides.

    x² - 4x + 4 = 7 + 4

    x² - 4x + 4 = 11

    Step 3: Factor left side.

    (x-2) ² = 11

    Step 4: Take square root.

    x - 2 = ±√11

    Step 5: Add 2 to both sides.

    x - 2 + 2 = 2 ±√11

    x = 2 ±√11

    x = 2 + √11 or x = 2 - √11
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