Basic Math Examples

$(\sqrt{x} - 5 \sqrt{2}) (\sqrt{x} + 5 \sqrt{2}) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$\sqrt{x} - 5 \sqrt{2} = 0$

$\sqrt{x} + 5 \sqrt{2} = 0$

Step 2

Set $\sqrt{x} - 5 \sqrt{2}$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $\sqrt{x} - 5 \sqrt{2}$ equal to $0$ .

$\sqrt{x} - 5 \sqrt{2} = 0$

Step 2.2

Solve $\sqrt{x} - 5 \sqrt{2} = 0$ for $x$ .

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Step 2.2.1

Add $5 \sqrt{2}$ to both sides of the equation.

$\sqrt{x} = 5 \sqrt{2}$

Step 2.2.2

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

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

Step 2.2.3

Simplify each side of the equation.

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Step 2.2.3.1

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

${(x^{\frac{1}{2}})}^{2} = {(5 \sqrt{2})}^{2}$

Step 2.2.3.2

Simplify the left side.

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Step 2.2.3.2.1

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

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Step 2.2.3.2.1.1

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

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Step 2.2.3.2.1.1.1

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

$x^{\frac{1}{2} \cdot 2} = {(5 \sqrt{2})}^{2}$

Step 2.2.3.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.3.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(5 \sqrt{2})}^{2}$

Step 2.2.3.2.1.1.2.2

Rewrite the expression.

$x^{1} = {(5 \sqrt{2})}^{2}$

Step 2.2.3.2.1.2

Simplify.

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

Step 2.2.3.3

Simplify the right side.

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Step 2.2.3.3.1

Simplify ${(5 \sqrt{2})}^{2}$ .

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Step 2.2.3.3.1.1

Simplify the expression.

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Step 2.2.3.3.1.1.1

Apply the product rule to $5 \sqrt{2}$ .

$x = 5^{2} {\sqrt{2}}^{2}$

Step 2.2.3.3.1.1.2

Raise $5$ to the power of $2$ .

$x = 25 {\sqrt{2}}^{2}$

Step 2.2.3.3.1.2

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

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Step 2.2.3.3.1.2.1

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

$x = 25 {(2^{\frac{1}{2}})}^{2}$

Step 2.2.3.3.1.2.2

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

$x = 25 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 2.2.3.3.1.2.3

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

$x = 25 \cdot 2^{\frac{2}{2}}$

Step 2.2.3.3.1.2.4

Cancel the common factor of $2$ .

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Step 2.2.3.3.1.2.4.1

Cancel the common factor.

$x = 25 \cdot 2^{\frac{2}{2}}$

Step 2.2.3.3.1.2.4.2

Rewrite the expression.

$x = 25 \cdot 2^{1}$

Step 2.2.3.3.1.2.5

Evaluate the exponent.

$x = 25 \cdot 2$

Step 2.2.3.3.1.3

Multiply $25$ by $2$ .

$x = 50$

Step 3

The final solution is all the values that make $(\sqrt{x} - 5 \sqrt{2}) (\sqrt{x} + 5 \sqrt{2}) = 0$ true.

$x = 50$