Algebra Examples

$4 \sqrt{x} - 1 = 3$

Step 1

Subtract $3$ from both sides of the equation.

$4 \sqrt{x} - 1 - 3 = 0$

Step 2

Subtract $3$ from $- 1$ .

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

Step 3

Factor $4$ out of $4 \sqrt{x} - 4$ .

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Step 3.1

Factor $4$ out of $4 \sqrt{x}$ .

$4 (\sqrt{x}) - 4 = 0$

Step 3.2

Factor $4$ out of $- 4$ .

$4 (\sqrt{x}) + 4 (- 1) = 0$

Step 3.3

Factor $4$ out of $4 (\sqrt{x}) + 4 (- 1)$ .

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

Step 4

Divide each term in $4 (\sqrt{x} - 1) = 0$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 (\sqrt{x} - 1) = 0$ by $4$ .

$\frac{4 (\sqrt{x} - 1)}{4} = \frac{0}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 (\sqrt{x} - 1)}{4} = \frac{0}{4}$

Step 4.2.1.2

Divide $\sqrt{x} - 1$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $4$ .

$\sqrt{x} - 1 = 0$

Step 5

Add $1$ to both sides of the equation.

$\sqrt{x} = 1$

Step 6

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

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

Step 7

Simplify each side of the equation.

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Step 7.1

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

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

Step 7.2

Simplify the left side.

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Step 7.2.1

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

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Step 7.2.1.1

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

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Step 7.2.1.1.1

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

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

Step 7.2.1.1.2

Cancel the common factor of $2$ .

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Step 7.2.1.1.2.1

Cancel the common factor.

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

Step 7.2.1.1.2.2

Rewrite the expression.

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

Step 7.2.1.2

Simplify.

$x = 1^{2}$

Step 7.3

Simplify the right side.

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Step 7.3.1

One to any power is one.

$x = 1$