Solve for x -1/5x^2+4=-1

$- \frac{1}{5} x^{2} + 4 = - 1$

Combine $x^{2}$ and $\frac{1}{5}$ .

$- \frac{x^{2}}{5} + 4 = - 1$

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

Subtract $4$ from both sides of the equation.

$- \frac{x^{2}}{5} = - 1 - 4$

Subtract $4$ from $- 1$ .

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

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{x^{2}}{5}) = - 5 \cdot - 5$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 5 (- \frac{x^{2}}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{x^{2}}{5}$ into the numerator.

$- 5 \frac{- x^{2}}{5} = - 5 \cdot - 5$

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- x^{2}}{5} = - 5 \cdot - 5$

Cancel the common factor.

$5 \cdot - 1 \frac{- x^{2}}{5} = - 5 \cdot - 5$

Rewrite the expression.

$- - x^{2} = - 5 \cdot - 5$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 5 \cdot - 5$

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

$x^{2} = - 5 \cdot - 5$

Simplify the right side.

Multiply $- 5$ by $- 5$ .

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

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

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

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$