Algebra Examples

$\sqrt{x} + 2 \sqrt{3} = 0$

Step 1

Subtract $2 \sqrt{3}$ from both sides of the equation.

$\sqrt{x} = - 2 \sqrt{3}$

Step 2

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

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

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

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

Step 3.2.1.2

Simplify.

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(- 2 \sqrt{3})}^{2}$ .

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Step 3.3.1.1

Simplify the expression.

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Step 3.3.1.1.1

Apply the product rule to $- 2 \sqrt{3}$ .

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

Step 3.3.1.1.2

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

$x = 4 {\sqrt{3}}^{2}$

Step 3.3.1.2

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x = 4 {(3^{\frac{1}{2}})}^{2}$

Step 3.3.1.2.2

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

$x = 4 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 3.3.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$x = 4 \cdot 3^{\frac{2}{2}}$

Step 3.3.1.2.4

Cancel the common factor of $2$ .

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Step 3.3.1.2.4.1

Cancel the common factor.

$x = 4 \cdot 3^{\frac{2}{2}}$

Step 3.3.1.2.4.2

Rewrite the expression.

$x = 4 \cdot 3^{1}$

Step 3.3.1.2.5

Evaluate the exponent.

$x = 4 \cdot 3$

Step 3.3.1.3

Multiply $4$ by $3$ .

$x = 12$

Step 4

Exclude the solutions that do not make $\sqrt{x} + 2 \sqrt{3} = 0$ true.

$No solution$