How do you solve using the completing the square method # x^2 + 7x – 9 = 0#?

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Answer 1 · 2016-03-15T08:43:37

Answer: #x=-7/2+-sqrt(85)/2# or #x approx -8.11 or 1.11#

To solve by completing the square, first add 9 to both sides

#x^2+7x=9#

Then you have to manipulate the number in front of #x#, in this case 7. You divide it by two and square the result, giving you

#(7/2)^2=49/4#

Add this to both sides of the above equation, giving

#x^2+7x+(7/2)^2=9+(7/2)^2#

This creates a perfect square on the left, such that

#(x+7/2)^2 = 85/4#

Take the square root of both sides, giving

#x+7/2=+-sqrt(85)/2#

Don't forget that #+-# in front of your square root operation! Now simply subtract #7/2# from both sides.

#x=-7/2+-sqrt(85)/2#

Plugging that into a calculator gives:

#x approx -8.11# or #x approx 1.11#