Question

$2x {}^{2} + 4x + 1 = 0$
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Answer 1

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2x² + 4x + 1 = 0

By adding 1 to each sides,

$2x^{2} + 4x + 1 + 1 = 0 + 1$

$2x^{2} + 4x +2= 1$

Divide both the sides by 2,

$\frac{2x {}^{2} }{2} + \frac{4x}{2} + \frac{2}{2} = \frac{1}{2}$

${x}^{2} + 2x + 1 = \frac{1}{2}$

Now, We get;

${x}^{2} + 2x + 1 = {(x + 1)}^{2}$

$( {x + 1)}^{2} = \frac{1}{2}$

Take square root in each sides,

$x + 1 = \frac{1}{ \sqrt{2} }$

$x = \frac{1}{ \sqrt{2} } - 1 = \frac{ \sqrt{2} - 2}{2}$

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Answer 2

Step-by-step explanation:

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