Algebra Examples

$f (x) = \sqrt{4 x} - 1$

Step 1

Set $\sqrt{4 x} - 1$ equal to $0$ .

$\sqrt{4 x} - 1 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $1$ to both sides of the equation.

$\sqrt{4 x} = 1$

Step 2.2

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

${\sqrt{4 x}}^{2} = 1^{2}$

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 $\sqrt{4 x}$ as ${(4 x)}^{\frac{1}{2}}$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Simplify ${({(4 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.3.2.1.1

Multiply the exponents in ${({(4 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.3.2.1.1.1

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

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

Step 2.3.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.3.2.1.1.2.1

Cancel the common factor.

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

Step 2.3.2.1.1.2.2

Rewrite the expression.

${(4 x)}^{1} = 1^{2}$

Step 2.3.2.1.2

Simplify.

$4 x = 1^{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

One to any power is one.

$4 x = 1$

Step 2.4

Divide each term in $4 x = 1$ by $4$ and simplify.

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Step 2.4.1

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $4$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{4}$

Step 3