Solve Using the Square Root Property 5(x^2-5)+8=3

$5 (x^{2} - 5) + 8 = 3$

Step 1

Simplify $5 (x^{2} - 5) + 8$ .

Simplify each term.

Apply the distributive property.

$5 x^{2} + 5 \cdot - 5 + 8 = 3$

Multiply $5$ by $- 5$ .

$5 x^{2} - 25 + 8 = 3$

Add $- 25$ and $8$ .

$5 x^{2} - 17 = 3$

Step 2

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

Add $17$ to both sides of the equation.

$5 x^{2} = 3 + 17$

Add $3$ and $17$ .

$5 x^{2} = 20$

Step 3

Divide each term in $5 x^{2} = 20$ by $5$ and simplify.

Divide each term in $5 x^{2} = 20$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{20}{5}$

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

$x^{2} = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x^{2} = 4$

Step 4

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

$x = \pm \sqrt{4}$

Step 5

Simplify $\pm \sqrt{4}$ .

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

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

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

$x = \pm 2$

Step 6

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

Solve Using the Square Root Property 5(x^2-5)+8=3

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