rewrite the equation by completing the square x^2+11x+24=0

x² + 11x + 24 = 0 , there are some guiding laws that need to be applied when using the completing the square method . There will be non time for me here to start discussing the laws, but will be explicity enough to be understood.

x² + 11x = 24

Now you add to both side of the equation the square of the half I'd the coefficient of x which is 11 and not coefficient of x² please note.

x² + 11x + (11/2)² = 24 + (11/2)²

We therefore have nothing to do with 11x.

x² + (11/2)² = 24 + 121/4

( x + 11/2 )² = 24 + 121/4 , now solve the expression on the right hand side fractionally. Which I believed you could solve now becomes

( x + 11/2 )² = 217/4

Now to solve for x, we revert back to the laws of indices by taking the square roots of both side

√( x + 11/2 )² = +/-√217/4

x + 11/2 = +/-√217

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2

x = -11/2 +/- √217

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2

x = -11 2 + 14.7/2 or -11/2 - 14.7/2