Basic Math Examples

$4 {(9 - x)}^{0.5} - 6 = 10$

Step 1

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

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Step 1.1

Add $6$ to both sides of the equation.

$4 {(9 - x)}^{0.5} = 10 + 6$

Step 1.2

Add $10$ and $6$ .

$4 {(9 - x)}^{0.5} = 16$

Step 2

Divide each term in $4 {(9 - x)}^{0.5} = 16$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 {(9 - x)}^{0.5} = 16$ by $4$ .

$\frac{4 {(9 - x)}^{0.5}}{4} = \frac{16}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 {(9 - x)}^{0.5}}{4} = \frac{16}{4}$

Step 2.2.1.2

Divide ${(9 - x)}^{0.5}$ by $1$ .

${(9 - x)}^{0.5} = \frac{16}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $16$ by $4$ .

${(9 - x)}^{0.5} = 4$

Step 3

Convert the decimal exponent to a fractional exponent.

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Step 3.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is $1$ number to the right of the decimal point, place the decimal number over $10^{1}$ $(10)$ . Next, add the whole number to the left of the decimal.

${(9 - x)}^{0 \frac{5}{10}} = 4$

Step 3.2

Reduce the fraction.

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Step 3.2.1

Convert $0 \frac{5}{10}$ to an improper fraction.

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Step 3.2.1.1

A mixed number is an addition of its whole and fractional parts.

${(9 - x)}^{0 + \frac{5}{10}} = 4$

Step 3.2.1.2

Add $0$ and $\frac{5}{10}$ .

${(9 - x)}^{\frac{5}{10}} = 4$

Step 3.2.2

Cancel the common factor of $5$ and $10$ .

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Step 3.2.2.1

Factor $5$ out of $5$ .

${(9 - x)}^{\frac{5 (1)}{10}} = 4$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $5$ out of $10$ .

${(9 - x)}^{\frac{5 \cdot 1}{5 \cdot 2}} = 4$

Step 3.2.2.2.2

Cancel the common factor.

${(9 - x)}^{\frac{5 \cdot 1}{5 \cdot 2}} = 4$

Step 3.2.2.2.3

Rewrite the expression.

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

Step 4

Raise each side of the equation to the power of $\frac{1}{0.5}$ to eliminate the fractional exponent on the left side.

${({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5

Simplify the exponent.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify ${({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}}$ .

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Step 5.1.1.1

Multiply the exponents in ${({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}}$ .

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Step 5.1.1.1.1

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

${(9 - x)}^{\frac{1}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.2

Cancel the common factor of $0.5$ .

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Step 5.1.1.1.2.1

Factor $0.5$ out of $1$ .

${(9 - x)}^{\frac{0.5 (2)}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.2.2

Cancel the common factor.

${(9 - x)}^{\frac{0.5 \cdot 2}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.2.3

Rewrite the expression.

${(9 - x)}^{\frac{2}{2}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.3

Divide $2$ by $2$ .

${(9 - x)}^{1} = 4^{\frac{1}{0.5}}$

Step 5.1.1.2

Simplify.

$9 - x = 4^{\frac{1}{0.5}}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $4^{\frac{1}{0.5}}$ .

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Step 5.2.1.1

Divide $1$ by $0.5$ .

$9 - x = 4^{2}$

Step 5.2.1.2

Raise $4$ to the power of $2$ .

$9 - x = 16$

Step 6

Solve for $x$ .

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Step 6.1

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

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Step 6.1.1

Subtract $9$ from both sides of the equation.

$- x = 16 - 9$

Step 6.1.2

Subtract $9$ from $16$ .

$- x = 7$

Step 6.2

Divide each term in $- x = 7$ by $- 1$ and simplify.

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Step 6.2.1

Divide each term in $- x = 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{7}{- 1}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{7}{- 1}$

Step 6.2.2.2

Divide $x$ by $1$ .

$x = \frac{7}{- 1}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $7$ by $- 1$ .

$x = - 7$