Question

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

Answer 1

Answer:

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)