Algebra Examples

$18 \sqrt{5 x} + 10$

Step 1

Set $18 \sqrt{5 x} + 10$ equal to $0$ .

$18 \sqrt{5 x} + 10 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $10$ from both sides of the equation.

$18 \sqrt{5 x} = - 10$

Step 2.2

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

${(18 \sqrt{5 x})}^{2} = {(- 10)}^{2}$

Step 2.3

Simplify each side of the equation.

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Step 2.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

${(18 {(5 x)}^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Simplify ${(18 {(5 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.3.2.1.1

Apply the product rule to $5 x$ .

${(18 (5^{\frac{1}{2}} x^{\frac{1}{2}}))}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.3.2.1.2.1

Apply the product rule to $18 \cdot 5^{\frac{1}{2}} x^{\frac{1}{2}}$ .

${(18 \cdot 5^{\frac{1}{2}})}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.2.2

Apply the product rule to $18 \cdot 5^{\frac{1}{2}}$ .

$18^{2} \cdot {(5^{\frac{1}{2}})}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.3

Raise $18$ to the power of $2$ .

$324 \cdot {(5^{\frac{1}{2}})}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.4

Multiply the exponents in ${(5^{\frac{1}{2}})}^{2}$ .

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Step 2.3.2.1.4.1

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

$324 \cdot 5^{\frac{1}{2} \cdot 2} {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.4.2

Cancel the common factor of $2$ .

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Step 2.3.2.1.4.2.1

Cancel the common factor.

$324 \cdot 5^{\frac{1}{2} \cdot 2} {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.4.2.2

Rewrite the expression.

$324 \cdot 5^{1} {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.5

Evaluate the exponent.

$324 \cdot 5 {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.6

Multiply $324$ by $5$ .

$1620 {(x^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

Step 2.3.2.1.7

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

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Step 2.3.2.1.7.1

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

$1620 x^{\frac{1}{2} \cdot 2} = {(- 10)}^{2}$

Step 2.3.2.1.7.2

Cancel the common factor of $2$ .

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Step 2.3.2.1.7.2.1

Cancel the common factor.

$1620 x^{\frac{1}{2} \cdot 2} = {(- 10)}^{2}$

Step 2.3.2.1.7.2.2

Rewrite the expression.

$1620 x^{1} = {(- 10)}^{2}$

Step 2.3.2.1.8

Simplify.

$1620 x = {(- 10)}^{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Raise $- 10$ to the power of $2$ .

$1620 x = 100$

Step 2.4

Divide each term in $1620 x = 100$ by $1620$ and simplify.

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Step 2.4.1

Divide each term in $1620 x = 100$ by $1620$ .

$\frac{1620 x}{1620} = \frac{100}{1620}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $1620$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{1620 x}{1620} = \frac{100}{1620}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{100}{1620}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Cancel the common factor of $100$ and $1620$ .

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Step 2.4.3.1.1

Factor $20$ out of $100$ .

$x = \frac{20 (5)}{1620}$

Step 2.4.3.1.2

Cancel the common factors.

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Step 2.4.3.1.2.1

Factor $20$ out of $1620$ .

$x = \frac{20 \cdot 5}{20 \cdot 81}$

Step 2.4.3.1.2.2

Cancel the common factor.

$x = \frac{20 \cdot 5}{20 \cdot 81}$

Step 2.4.3.1.2.3

Rewrite the expression.

$x = \frac{5}{81}$

Step 2.5

Exclude the solutions that do not make $18 \sqrt{5 x} + 10 = 0$ true.

$No solution$