The equation resulting from completing the square and the factoring x² + 4x = 7, we get (x + 2 + √11)(x + 2 - √11).
The formulas that are used in factoring are:-
In the question, we are asked to find the equation that results from completing the square and then factoring the equation x² + 4x = 7.
To complete the square on the left side, we will use the formula (a + b)² = a² + 2ab + b², as follows:
x² + 4x = 7,
or, x² + 2(2)x = 7
Comparing 2(2)x with 2ab, we get a = 2, and b = x.
To complete the square on the left side, we add 2² to both side of the equation as follows:
x² + 2(2)x + 2² = 7 + 2²,
or, (x + 2)² = 11,
or, (x + 2)² - 11 = 0,
or, (x + 2)² - (√11)² = 0.
Now, to factor, we use the formula a² - b² = (a + b)(a - b) as follows:
(x + 2)² - (√11)² = 0,
or, (x + 2 + √11)(x + 2 - √11) = 0.
Thus, the equation resulting from completing the square and the factoring x² + 4x = 7, we get (x + 2 + √11)(x + 2 - √11).
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