Solve by completing the square :  x^2 +9x -5 = 0

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We have to solve x^2 +9x -5 = 0

x^2 +9x -5 = 0

=> x^2 + 9x + (9/2)^2 - 5 - (9/2)^2 =0

=> [x + (9/2)]^2 - 25.25 = 0

=> [x + (9/2)]^2 = 25.25

x + 9/2 = + sqrt (25.25) and  sqrt (25.25)

x = -4.5 + sqrt (25.25) and -4.5- sqrt (25.25)

Therefore x = -4.5 + sqrt (25.25) and -4.5- sqrt (25.25)

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Given the quadratic function:

x^2 + 9x -5 = 0

We need to solve by completing the square.

First we will group terms.

==. (x^2 + 9x ) -5 = 0

Now we will move 5 to the right side.

==> (x^2 + 9x) = 5

Now we will complete the square for x^2 + 9x

We will add (9/2)^2 to both sides.

==> (9/2)^2 = 81/4

==> (x^2 + 9x + 81/4 = 5 + 81/4

==> ( x +9/2)^2 = (20+81)/4

==> (x+9/2)^2 = (101)/4

Take the square root of both sides.

==> x+9/2 = +-sqrt101 / 2

=> x = +-sqrt101/2  - 9/2

==> x1 = (-9 + sqrt101)/2

==> x2= (-9 - sqrt101)/2

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