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 $x approx 1.11$

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