Basic Math Examples

$4 + 3 \sqrt{4 - 3 w} = 13$

Step 1

Move all terms not containing $3 \sqrt{4 - 3 w}$ to the right side of the equation.

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Step 1.1

Subtract $4$ from both sides of the equation.

$3 \sqrt{4 - 3 w} = 13 - 4$

Step 1.2

Subtract $4$ from $13$ .

$3 \sqrt{4 - 3 w} = 9$

Step 2

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

${(3 \sqrt{4 - 3 w})}^{2} = 9^{2}$

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 $\sqrt{4 - 3 w}$ as ${(4 - 3 w)}^{\frac{1}{2}}$ .

${(3 {(4 - 3 w)}^{\frac{1}{2}})}^{2} = 9^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(3 {(4 - 3 w)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $3 {(4 - 3 w)}^{\frac{1}{2}}$ .

$3^{2} {({(4 - 3 w)}^{\frac{1}{2}})}^{2} = 9^{2}$

Step 3.2.1.2

Raise $3$ to the power of $2$ .

$9 {({(4 - 3 w)}^{\frac{1}{2}})}^{2} = 9^{2}$

Step 3.2.1.3

Multiply the exponents in ${({(4 - 3 w)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.3.1

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

$9 {(4 - 3 w)}^{\frac{1}{2} \cdot 2} = 9^{2}$

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.

$9 {(4 - 3 w)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$9 {(4 - 3 w)}^{1} = 9^{2}$

Step 3.2.1.4

Simplify.

$9 (4 - 3 w) = 9^{2}$

Step 3.2.1.5

Apply the distributive property.

$9 \cdot 4 + 9 (- 3 w) = 9^{2}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $9$ by $4$ .

$36 + 9 (- 3 w) = 9^{2}$

Step 3.2.1.6.2

Multiply $- 3$ by $9$ .

$36 - 27 w = 9^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $9$ to the power of $2$ .

$36 - 27 w = 81$

Step 4

Solve for $w$ .

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Step 4.1

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

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Step 4.1.1

Subtract $36$ from both sides of the equation.

$- 27 w = 81 - 36$

Step 4.1.2

Subtract $36$ from $81$ .

$- 27 w = 45$

Step 4.2

Divide each term in $- 27 w = 45$ by $- 27$ and simplify.

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Step 4.2.1

Divide each term in $- 27 w = 45$ by $- 27$ .

$\frac{- 27 w}{- 27} = \frac{45}{- 27}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 27$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 27 w}{- 27} = \frac{45}{- 27}$

Step 4.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{45}{- 27}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $45$ and $- 27$ .

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Step 4.2.3.1.1

Factor $9$ out of $45$ .

$w = \frac{9 (5)}{- 27}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $9$ out of $- 27$ .

$w = \frac{9 \cdot 5}{9 \cdot - 3}$

Step 4.2.3.1.2.2

Cancel the common factor.

$w = \frac{9 \cdot 5}{9 \cdot - 3}$

Step 4.2.3.1.2.3

Rewrite the expression.

$w = \frac{5}{- 3}$

Step 4.2.3.2

Move the negative in front of the fraction.

$w = - \frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{5}{3}$

Decimal Form:

$w = - 1.\overline{6}$

Mixed Number Form:

$w = - 1 \frac{2}{3}$