Precalculus Examples

\sqrt{x - 10} - 4 = 0

$\sqrt{x - 10} - 4 = 0$

Step 1

Add

4

$4$ to both sides of the equation.

\sqrt{x - 10} = 4

$\sqrt{x - 10} = 4$

Step 2

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

{\sqrt{x - 10}}^{2} = 4^{2}

${\sqrt{x - 10}}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use

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

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

\sqrt{x - 10}

$\sqrt{x - 10}$ as

{(x - 10)}^{\frac{1}{2}}

${(x - 10)}^{\frac{1}{2}}$ .

{({(x - 10)}^{\frac{1}{2}})}^{2} = 4^{2}

${({(x - 10)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify

{({(x - 10)}^{\frac{1}{2}})}^{2}

${({(x - 10)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in

{({(x - 10)}^{\frac{1}{2}})}^{2}

${({(x - 10)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

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 - 10)}^{\frac{1}{2} \cdot 2} = 4^{2}

${(x - 10)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 3.2.1.1.2

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${(x - 10)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(x - 10)}^{1} = 4^{2}$

${(x - 10)}^{1} = 4^{2}$

${(x - 10)}^{1} = 4^{2}$

Step 3.2.1.2

Simplify.

$x - 10 = 4^{2}$

$x - 10 = 4^{2}$

$x - 10 = 4^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Raise

$4$ to the power of

$2$ .

$x - 10 = 16$

$x - 10 = 16$

$x - 10 = 16$

Step 4

Move all terms not containing

$x$ to the right side of the equation.

Tap for more steps...

Step 4.1

Add

$10$ to both sides of the equation.

$x = 16 + 10$

Step 4.2

Add

$16$ and

$10$ .

$x = 26$

$x = 26$

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