Algebra Examples

$- 3 \sqrt{x} - 8 = 19$

Step 1

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

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Step 1.1

Add $8$ to both sides of the equation.

$- 3 \sqrt{x} = 19 + 8$

Step 1.2

Add $19$ and $8$ .

$- 3 \sqrt{x} = 27$

Step 2

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

${(- 3 \sqrt{x})}^{2} = 27^{2}$

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 $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(- 3 x^{\frac{1}{2}})}^{2} = 27^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Apply the product rule to $- 3 x^{\frac{1}{2}}$ .

${(- 3)}^{2} {(x^{\frac{1}{2}})}^{2} = 27^{2}$

Step 3.2.1.2

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

$9 {(x^{\frac{1}{2}})}^{2} = 27^{2}$

Step 3.2.1.3

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

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Step 3.2.1.3.1

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

$9 x^{\frac{1}{2} \cdot 2} = 27^{2}$

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.

$9 x^{\frac{1}{2} \cdot 2} = 27^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$9 x^{1} = 27^{2}$

Step 3.2.1.4

Simplify.

$9 x = 27^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $27$ to the power of $2$ .

$9 x = 729$

Step 4

Divide each term in $9 x = 729$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 x = 729$ by $9$ .

$\frac{9 x}{9} = \frac{729}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{729}{9}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{729}{9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $729$ by $9$ .

$x = 81$

Step 5

Exclude the solutions that do not make $- 3 \sqrt{x} - 8 = 19$ true.

$No solution$