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

1 Answer
Jim G.
May 23, 2016

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 = -4rArr(-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

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