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29 December, 17:02

What number must you add to complete the square x^2+4x=15

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  1. 29 December, 17:19
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    Since we want it in the form: (x - a) ², let's first expand (x - a) ² and then equate for the coefficients.

    (x - a) ² = x² - 2ax + a²

    x² + 4x - 15 = x² - 2ax + a²

    Now, let's focus on the middle term.

    4x = - 2ax

    4 = - 2a

    a = - 2

    Thus, we know that a = - 2

    Then, we can say (x + 2) ² = x² + 4x - 15

    x² + 4x + 4 = x² + 4x - 15

    Thus, 19 units are needed in order to complete the square to produce:

    (x + 2) ²
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