Pre-Algebra Examples

$x = - 46 + \sqrt{- 46^{2 - 4 (2 (252))}}$

Step 1

Multiply $- 4 \cdot 2 \cdot 252$ .

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Step 1.1

Multiply $- 4$ by $2$ .

$x = - 46 + \sqrt{- 46^{2 - 8 \cdot 252}}$

Step 1.2

Multiply $- 8$ by $252$ .

$x = - 46 + \sqrt{- 46^{2 - 2016}}$

Step 2

Subtract $2016$ from $2$ .

$x = - 46 + \sqrt{- 46^{- 2014}}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = - 46 + \sqrt{- \frac{1}{46^{2014}}}$

Step 4

Rewrite $- \frac{1}{46^{2014}}$ as ${(\frac{i}{46^{1007}})}^{2}$ .

$x = - 46 + \sqrt{{(\frac{i}{46^{1007}})}^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$x = - 46 + \frac{i}{46^{1007}}$