Solve Using the Square Root Property 8x^2+5=35

$8 x^{2} + 5 = 35$

Step 1

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

Subtract $5$ from both sides of the equation.

$8 x^{2} = 35 - 5$

Subtract $5$ from $35$ .

$8 x^{2} = 30$

Step 2

Divide each term in $8 x^{2} = 30$ by $8$ and simplify.

Divide each term in $8 x^{2} = 30$ by $8$ .

$\frac{8 x^{2}}{8} = \frac{30}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x^{2}}{8} = \frac{30}{8}$

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

$x^{2} = \frac{30}{8}$

Simplify the right side.

Cancel the common factor of $30$ and $8$ .

Factor $2$ out of $30$ .

$x^{2} = \frac{2 (15)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$x^{2} = \frac{2 \cdot 15}{2 \cdot 4}$

Cancel the common factor.

$x^{2} = \frac{2 \cdot 15}{2 \cdot 4}$

Rewrite the expression.

$x^{2} = \frac{15}{4}$

Step 3

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

$x = \pm \sqrt{\frac{15}{4}}$

Step 4

Simplify $\pm \sqrt{\frac{15}{4}}$ .

Rewrite $\sqrt{\frac{15}{4}}$ as $\frac{\sqrt{15}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{15}}{\sqrt{4}}$

Simplify the denominator.

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

$x = \pm \frac{\sqrt{15}}{\sqrt{2^{2}}}$

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

$x = \pm \frac{\sqrt{15}}{2}$

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.

$x = \frac{\sqrt{15}}{2}$

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

$x = - \frac{\sqrt{15}}{2}$

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

$x = \frac{\sqrt{15}}{2}, - \frac{\sqrt{15}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{15}}{2}, - \frac{\sqrt{15}}{2}$

Decimal Form:

$x = 1.93649167 \dots, - 1.93649167 \dots$

Solve Using the Square Root Property 8x^2+5=35

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