Solve Using the Square Root Property 8x^2-3=597

$8 x^{2} - 3 = 597$

Step 1

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

Add $3$ to both sides of the equation.

$8 x^{2} = 597 + 3$

Add $597$ and $3$ .

$8 x^{2} = 600$

Step 2

Divide each term in $8 x^{2} = 600$ by $8$ and simplify.

Divide each term in $8 x^{2} = 600$ by $8$ .

$\frac{8 x^{2}}{8} = \frac{600}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x^{2}}{8} = \frac{600}{8}$

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

$x^{2} = \frac{600}{8}$

Simplify the right side.

Divide $600$ by $8$ .

$x^{2} = 75$

Step 3

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

$x = \pm \sqrt{75}$

Step 4

Simplify $\pm \sqrt{75}$ .

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$x = \pm \sqrt{25 (3)}$

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm 5 \sqrt{3}$

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.

$x = 5 \sqrt{3}$

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

$x = - 5 \sqrt{3}$

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

$x = 5 \sqrt{3}, - 5 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 5 \sqrt{3}, - 5 \sqrt{3}$

Decimal Form:

$x = 8.66025403 \dots, - 8.66025403 \dots$

Solve Using the Square Root Property 8x^2-3=597

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