x^2 + x + 14 = 0 ⇒x^2 + x2 + x2 + 14 = 0 ⇒ x ( x + 12) + 12( x + 12) = 0 ⇒( x + 12) ( x + 12) = 0 ⇒ x = 12, 12 ...

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Uses of Ratios and Proportions

Solve; x2+x+...

Question

Solve;
$x^{2} + x + \frac{1}{4} = 0$

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Solution

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

$\Rightarrow x^{2} + \frac{x}{2} + \frac{x}{2} + \frac{1}{4} = 0$

$\Rightarrow x (x + \frac{1}{2}) + \frac{1}{2} (x + \frac{1}{2}) = 0$

$\Rightarrow (x + \frac{1}{2}) (x + \frac{1}{2}) = 0$

$\Rightarrow x = - \frac{1}{2}, - \frac{1}{2}$

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