Pre-Algebra Examples

$t = - \frac{(- 96) (\sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})}{2 (16)}$

Step 1

Multiply $- 96$ by $\sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}$ .

$t = - \frac{- 96 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}}{2 (16)}$

Step 2

Multiply $- 96$ by $\sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}$ .

$t = - \frac{- 96 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}}{2 (16)}$

Step 3

Simplify $- \frac{- 96 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}}{2 (16)}$ .

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Step 3.1

Cancel the common factor of $- 96$ and $2$ .

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Step 3.1.1

Factor $2$ out of $- 96 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}$ .

$t = - \frac{2 (- 48 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})}{2 (16)}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Cancel the common factor.

$t = - \frac{2 (- 48 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})}{2 \cdot 16}$

Step 3.1.2.2

Rewrite the expression.

$t = - \frac{- 48 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}}{16}$

Step 3.2

Cancel the common factor of $- 48$ and $16$ .

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Step 3.2.1

Factor $16$ out of $- 48 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}$ .

$t = - \frac{16 (- 3 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})}{16}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $16$ out of $16$ .

$t = - \frac{16 (- 3 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})}{16 (1)}$

Step 3.2.2.2

Cancel the common factor.

$t = - \frac{16 (- 3 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})}{16 \cdot 1}$

Step 3.2.2.3

Rewrite the expression.

$t = - \frac{- 3 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}}{1}$

Step 3.2.2.4

Divide $- 3 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128}$ by $1$ .

$t = - (- 3 \sqrt{{(- 96)}^{2} - 4 \cdot 16 \cdot 128})$

Step 3.3

Raise $- 96$ to the power of $2$ .

$t = - (- 3 \sqrt{9216 - 4 \cdot 16 \cdot 128})$

Step 3.4

Multiply $- 4 \cdot 16 \cdot 128$ .

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Step 3.4.1

Multiply $- 4$ by $16$ .

$t = - (- 3 \sqrt{9216 - 64 \cdot 128})$

Step 3.4.2

Multiply $- 64$ by $128$ .

$t = - (- 3 \sqrt{9216 - 8192})$

Step 3.5

Subtract $8192$ from $9216$ .

$t = - (- 3 \sqrt{1024})$

Step 3.6

Rewrite $1024$ as $32^{2}$ .

$t = - (- 3 \sqrt{32^{2}})$

Step 3.7

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

$t = - (- 3 \cdot 32)$

Step 3.8

Multiply $- (- 3 \cdot 32)$ .

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Step 3.8.1

Multiply $- 3$ by $32$ .

$t = - - 96$

Step 3.8.2

Multiply $- 1$ by $- 96$ .

$t = 96$