Solve Using the Square Root Property 9x^2-5=607

$9 x^{2} - 5 = 607$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $5$ to both sides of the equation.

$9 x^{2} = 607 + 5$

Add $607$ and $5$ .

$9 x^{2} = 612$

Step 2

Divide each term in $9 x^{2} = 612$ by $9$ and simplify.

Divide each term in $9 x^{2} = 612$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{612}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{612}{9}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{612}{9}$

Simplify the right side.

Divide $612$ by $9$ .

$x^{2} = 68$

Step 3

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

$x = \pm \sqrt{68}$

Step 4

Simplify $\pm \sqrt{68}$ .

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$x = \pm \sqrt{4 (17)}$

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2} \cdot 17}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{17}$

Step 5

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

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 \sqrt{17}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 \sqrt{17}$

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

$x = 2 \sqrt{17}, - 2 \sqrt{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{17}, - 2 \sqrt{17}$

Decimal Form:

$x = 8.24621125 \dots, - 8.24621125 \dots$

Solve Using the Square Root Property 9x^2-5=607

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