Precalculus Examples

x^{2} + 9 = 73

$x^{2} + 9 = 73$

Step 1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 1.1

Subtract

9

$9$ from both sides of the equation.

x^{2} = 73 - 9

$x^{2} = 73 - 9$

Step 1.2

Subtract

9

$9$ from

73

$73$ .

x^{2} = 64

$x^{2} = 64$

x^{2} = 64

$x^{2} = 64$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x = \pm \sqrt{64}

$x = \pm \sqrt{64}$

Step 3

Simplify

\pm \sqrt{64}

$\pm \sqrt{64}$ .

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Step 3.1

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

x = \pm \sqrt{8^{2}}

$x = \pm \sqrt{8^{2}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

x = \pm 8

$x = \pm 8$

x = \pm 8

$x = \pm 8$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x = 8

$x = 8$

Step 4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 8

$x = - 8$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

x = 8, - 8

$x = 8, - 8$

x = 8, - 8

$x = 8, - 8$

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