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garik1379 [7]
3 years ago
8

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

Mathematics
1 answer:
Andrew [12]3 years ago
6 0
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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