Question

How do you solve `x(x - 4) = 45` by completing the square?

Answer 1

x = -5 , x= 9

Explanation:

Since this is a quadratic equation expand brackets and equate to zero.

`rArrx^2-4x-45=0`

This is now in standard form : `ax^2+bx+c=0`

To complete the square add on `(b/2)^2`

here b = -4`rArr(-4/2)^2=4`

equation can now be written as

`[x^2-4x+4]+(-4)-45=0`

Since we added on 4 to complete the square we must -4

`rArr(x-2)^2-4-45=0rArr(x-2)^2=49`

Taking the square root of both sides.

`x-2=±sqrt49=±7`

hence x = 7 + 2 = 9 or x = -7 + 2 =-5