Basic Math Examples

$- 2 \sqrt{7 B - 14} - 16 = - 18$

Step 1

Move all terms not containing $- 2 \sqrt{7 B - 14}$ to the right side of the equation.

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Step 1.1

Add $16$ to both sides of the equation.

$- 2 \sqrt{7 B - 14} = - 18 + 16$

Step 1.2

Add $- 18$ and $16$ .

$- 2 \sqrt{7 B - 14} = - 2$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${(- 2 \sqrt{7 B - 14})}^{2} = {(- 2)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 B - 14}$ as ${(7 B - 14)}^{\frac{1}{2}}$ .

${(- 2 {(7 B - 14)}^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- 2 {(7 B - 14)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $- 2 {(7 B - 14)}^{\frac{1}{2}}$ .

${(- 2)}^{2} {({(7 B - 14)}^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Step 3.2.1.2

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

$4 {({(7 B - 14)}^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Step 3.2.1.3

Multiply the exponents in ${({(7 B - 14)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 {(7 B - 14)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$4 {(7 B - 14)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$4 {(7 B - 14)}^{1} = {(- 2)}^{2}$

Step 3.2.1.4

Simplify.

$4 (7 B - 14) = {(- 2)}^{2}$

Step 3.2.1.5

Apply the distributive property.

$4 (7 B) + 4 \cdot - 14 = {(- 2)}^{2}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $7$ by $4$ .

$28 B + 4 \cdot - 14 = {(- 2)}^{2}$

Step 3.2.1.6.2

Multiply $4$ by $- 14$ .

$28 B - 56 = {(- 2)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$28 B - 56 = 4$

Step 4

Solve for $B$ .

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Step 4.1

Move all terms not containing $B$ to the right side of the equation.

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Step 4.1.1

Add $56$ to both sides of the equation.

$28 B = 4 + 56$

Step 4.1.2

Add $4$ and $56$ .

$28 B = 60$

Step 4.2

Divide each term in $28 B = 60$ by $28$ and simplify.

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Step 4.2.1

Divide each term in $28 B = 60$ by $28$ .

$\frac{28 B}{28} = \frac{60}{28}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $28$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{28 B}{28} = \frac{60}{28}$

Step 4.2.2.1.2

Divide $B$ by $1$ .

$B = \frac{60}{28}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $60$ and $28$ .

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Step 4.2.3.1.1

Factor $4$ out of $60$ .

$B = \frac{4 (15)}{28}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $4$ out of $28$ .

$B = \frac{4 \cdot 15}{4 \cdot 7}$

Step 4.2.3.1.2.2

Cancel the common factor.

$B = \frac{4 \cdot 15}{4 \cdot 7}$

Step 4.2.3.1.2.3

Rewrite the expression.

$B = \frac{15}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$B = \frac{15}{7}$

Decimal Form:

$B = 2.\overline{142857}$

Mixed Number Form:

$B = 2 \frac{1}{7}$