Solve for x 5x^2+500=844.45

$5 x^{2} + 500 = 844.45$

Step 1

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

Subtract $500$ from both sides of the equation.

$5 x^{2} = 844.45 - 500$

Subtract $500$ from $844.45$ .

$5 x^{2} = 344.45$

Step 2

Divide each term in $5 x^{2} = 344.45$ by $5$ and simplify.

Divide each term in $5 x^{2} = 344.45$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{344.45}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{344.45}{5}$

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

$x^{2} = \frac{344.45}{5}$

Simplify the right side.

Divide $344.45$ by $5$ .

$x^{2} = 68.89$

Step 3

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

$x = \pm \sqrt{68.89}$

Step 4

Simplify $\pm \sqrt{68.89}$ .

Rewrite $68.89$ as ${8.3}^{2}$ .

$x = \pm \sqrt{{8.3}^{2}}$

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

$x = \pm 8.3$

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.

$x = 8.3$

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

$x = - 8.3$

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

$x = 8.3, - 8.3$