Question

Maya is solving the quadratic equation by completing the square.

Answer 1

Step-by-step explanation:

factor 4 out of the variable terms, as this helps.

but my approach is simply to define the target and then calculate "backwards".

we want to find

(ax + b)² = a²x² + 2abx + b²

and now we compare with the original equation :

a²x² = 4x²

a² = 4

a = 2

2abx = 16x

2×2×bx = 16x

4b = 16

b = 4

b² = 16, but we have only 3, so we need to subtract 16-3 = 13 from the completed square.

so, our equation is

(2x + 4)² - 13 = 0

(2x + 4)² = 13

2x + 4 = sqrt(13)

2x = sqrt(13) - 4

x = sqrt(13)/2 - 2