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How do we solve this?

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Answer 1 · 2017-08-31T02:29:30

$x = \sqrt{20} i ≅ 4.47 i$ $x=sqrt20 i ~= 4.47i$

Explanation:

$- 4 x^{2} - 80 = 0$ $-4x^2-80=0$

Add 80 to both sides:

$- 4 x^{2} = 80$ $-4x^2=80$

Multiply both sides by $- 1$ $-1$ :

$4 x^{2} = - 80$ $4x^2 = -80$

Divide both sides by $4$ $4$ :

$x^2 = cancel(-80)/cancel(4)=-20$

Now, with 'normal' numbers we cannot take the square root of a negative number, but with 'imaginary' numbers we can. The square root of $-1$ is written as $i$ :

$x^2 = 20xx-1$

$x=sqrt(20)xxsqrt(-1)$

$x=sqrt20 i ~= 4.47i$

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