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Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
$x^2 - 8x + 18 = 0$
Given:
Given quadratic equation is $x^2 - 8x + 18 = 0$.
To do:
We have to find the roots of the given quadratic equation.
Solution:
$x^2 - 8x + 18 = 0$
$x^2 + 2\times 4x = -18$
Adding $(4)^2$ on both sides completes the square. Therefore,
$x^2 + 2\times 4 x + (4)^2 = -18+(4)^2$
$(x+4)^2=-18+16$ (Since $(a+b)^2=a^2+2ab+b^2$)
$(x+4)^2=-2$
$x+4=\pm \sqrt{-2}$ (Taking square root on both sides)
$x=\sqrt{-2}-4$ or $x=-\sqrt{-2}-4$
Therefore, no real roots exist for the given quadratic equation.
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