Precalculus Examples

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

Step 1

Add $3$ to both sides of the equation.

$4 \sqrt{x} = 3$

Step 2

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

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

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Apply the product rule to $4 x^{\frac{1}{2}}$ .

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

Step 3.2.1.2

Raise $4$ to the power of $2$ .

$16 {(x^{\frac{1}{2}})}^{2} = 3^{2}$

Step 3.2.1.3

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

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Step 3.2.1.3.1

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

$16 x^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$16 x^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$16 x^{1} = 3^{2}$

Step 3.2.1.4

Simplify.

$16 x = 3^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $3$ to the power of $2$ .

$16 x = 9$

Step 4

Divide each term in $16 x = 9$ by $16$ and simplify.

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Step 4.1

Divide each term in $16 x = 9$ by $16$ .

$\frac{16 x}{16} = \frac{9}{16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{9}{16}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{16}$

Decimal Form:

$x = 0.5625$