Solve Using the Square Root Property 10x^2+2=282

$10 x^{2} + 2 = 282$

Step 1

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

Subtract $2$ from both sides of the equation.

$10 x^{2} = 282 - 2$

Subtract $2$ from $282$ .

$10 x^{2} = 280$

Step 2

Divide each term in $10 x^{2} = 280$ by $10$ and simplify.

Divide each term in $10 x^{2} = 280$ by $10$ .

$\frac{10 x^{2}}{10} = \frac{280}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x^{2}}{10} = \frac{280}{10}$

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

$x^{2} = \frac{280}{10}$

Simplify the right side.

Divide $280$ by $10$ .

$x^{2} = 28$

Step 3

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

$x = \pm \sqrt{28}$

Step 4

Simplify $\pm \sqrt{28}$ .

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$x = \pm \sqrt{4 (7)}$

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

$x = \pm \sqrt{2^{2} \cdot 7}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{7}$

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.

$x = 2 \sqrt{7}$

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

$x = - 2 \sqrt{7}$

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

$x = 2 \sqrt{7}, - 2 \sqrt{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{7}, - 2 \sqrt{7}$

Decimal Form:

$x = 5.29150262 \dots, - 5.29150262 \dots$

Solve Using the Square Root Property 10x^2+2=282

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