Solve the following equations by completing the square.
x2 + 4x = 21

x = 3 or -7

Step-by-step explanation:

Recall that for a quadratic equation in the form:

Ax² + Bx = C

we need to add (B/2)² to both sides of the equation to

In our case, we are given:

x² + 4x = 21    

compared to the general equation above, B = 4, hence we need to add (4/2)² to both sides

x² + 4x      = 21     (complete the square)

x² + 4x +   (4/2)²   = 21   + (4/2)²

x² + 4x +   2²   = 21   + 2²

(x+ 2)²   = 21   + 4

(x+ 2)²   = 25  (take square root of both sides)

(x+2) = ±√25

(x+2) = ±5

hence

(x+2) = +5> x = 5 - 2 = 3 (answer)

or

(x+2) = -5  > x = -5 - 2 = -7(answer)

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step-by-step explanation:

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