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

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Solution

Given quadratic equation is
$2 x squared plus x minus 4 equals 0 rightwards double arrow x squared plus 1 half x minus 2 equals 0 space rightwards double arrow x squared plus 2 cross times 1 fourth x plus left parenthesis 1 fourth right parenthesis squared minus left parenthesis 1 fourth right parenthesis squared minus 2 equals 0 rightwards double arrow left parenthesis x plus 1 fourth right parenthesis squared equals left parenthesis 1 fourth right parenthesis squared plus 2 equals 1 over 16 plus 2 equals 33 over 16 rightwards double arrow x plus 1 fourth equals plus-or-minus square root of 33 over 16 end root equals plus-or-minus fraction numerator square root of 33 over denominator 4 end fraction rightwards double arrow x equals negative 1 fourth plus-or-minus fraction numerator square root of 33 over denominator 4 end fraction rightwards double arrow x equals fraction numerator negative 1 minus square root of 33 over denominator 4 end fraction space o r space fraction numerator negative 1 plus square root of 33 over denominator 4 end fraction$

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Similar questions

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

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

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

2 x^{2} + x + 4 = 0

2 x^{2} - 7 x + 3 = 0

2 x^{2} + x - 4 = 0

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

2 x^{2} + x + 4 = 0

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