Question

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

Answer 1

x = 3 or -7

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)