Solve each of the following quadratic equations:
$x^{2} = 18 x - 77$

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Solution

$x^{2} = 18 x - 77$

$x^{2} - 18 x + 77 = 0$

$x^{2} - (11 + 7) x + 77 = 0$

$x^{2} - 11 x - 7 x + 77 = 0$

$x (x - 11) - 7 (x - 11) = 0$

$(x - 11) (x - 7) = 0$

$x - 11 = 0$
$x = 11$
and
$x - 7 = 0$
$x = 7$

so value of x is 11 and 7

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