Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$4 x^{2} + 4 \sqrt{3} x + 3 = 0$

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Solution

The given equation is
$4 x squared plus 4 square root of 3 x plus 3 equals 0 rightwards double arrow x squared plus square root of 3 x plus 3 over 4 equals 0 rightwards double arrow x squared plus 2 cross times fraction numerator square root of 3 over denominator 2 end fraction x plus 3 over 4 equals 0 rightwards double arrow left parenthesis x plus fraction numerator square root of 3 over denominator 2 end fraction right parenthesis squared equals 0 rightwards double arrow x equals negative fraction numerator square root of 3 over denominator 2 end fraction space comma negative fraction numerator square root of 3 over denominator 2 end fraction$

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Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$2 x^{2} + x - 4 = 0$

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0$

4 x^{2} + 4 \sqrt{3} x + 3 = 0

4 x^{2} + 4 \sqrt{3} x + 3 = 0

4 x^{2} + 4 \sqrt{3} x + 3 = 0

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