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Precalculus Examples

\sqrt{x} - 3 = 4

$\sqrt{x} - 3 = 4$

Step 1

Move all terms not containing

\sqrt{x}

$\sqrt{x}$ to the right side of the equation.

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Step 1.1

Add

3

$3$ to both sides of the equation.

\sqrt{x} = 4 + 3

$\sqrt{x} = 4 + 3$

Step 1.2

Add

4

$4$ and

3

$3$ .

\sqrt{x} = 7

$\sqrt{x} = 7$

\sqrt{x} = 7

$\sqrt{x} = 7$

Step 2

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

{\sqrt{x}}^{2} = 7^{2}

${\sqrt{x}}^{2} = 7^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{x}

$\sqrt{x}$ as

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

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

{(x^{\frac{1}{2}})}^{2} = 7^{2}

${(x^{\frac{1}{2}})}^{2} = 7^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify

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

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

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Step 3.2.1.1

Multiply the exponents in

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

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

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Step 3.2.1.1.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

x^{\frac{1}{2} \cdot 2} = 7^{2}

$x^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.2.1.1.2

Cancel the common factor of

2

$2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$x^{1} = 7^{2}$

$x^{1} = 7^{2}$

$x^{1} = 7^{2}$

Step 3.2.1.2

Simplify.

$x = 7^{2}$

$x = 7^{2}$

$x = 7^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise

$7$ to the power of

$2$ .

$x = 49$

$x = 49$

$x = 49$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$