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solve the equation for all values of x by completing the squarex²-12x=-23

Answer :

Solution

We can do the following:

[tex]x^2-12x+(\frac{12}{2})^2=-23+(\frac{12}{2})^2[/tex]

And if we simplify we got.

[tex]x^2-12x+36=-23+36[/tex][tex](x-6)^2=13[/tex]

Taking square root we got:

[tex]x-6=\pm\sqrt[]{13}[/tex]

Then the two solutions are:

[tex]x_1=-\sqrt[]{13}+6,x_2=\sqrt[]{13}+6[/tex]

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