Find the Roots (Zeros) f(x)=-1/5x^2-10

$f (x) = - \frac{1}{5} x^{2} - 10$

Step 1

Set $- \frac{1}{5} x^{2} - 10$ equal to $0$ .

$- \frac{1}{5} x^{2} - 10 = 0$

Step 2

Solve for $x$ .

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

$- \frac{x^{2}}{5} - 10 = 0$

Add $10$ to both sides of the equation.

$- \frac{x^{2}}{5} = 10$

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

$- 5 (- \frac{x^{2}}{5}) = - 5 \cdot 10$

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.

$- 5 \frac{- x^{2}}{5} = - 5 \cdot 10$

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- x^{2}}{5} = - 5 \cdot 10$

Cancel the common factor.

$5 \cdot - 1 \frac{- x^{2}}{5} = - 5 \cdot 10$

Rewrite the expression.

$- - x^{2} = - 5 \cdot 10$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 5 \cdot 10$

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

$x^{2} = - 5 \cdot 10$

Simplify the right side.

Multiply $- 5$ by $10$ .

$x^{2} = - 50$

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

$x = \pm \sqrt{- 50}$

Simplify $\pm \sqrt{- 50}$ .

Rewrite $- 50$ as $- 1 (50)$ .

$x = \pm \sqrt{- 1 (50)}$

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{50}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$x = \pm i \cdot \sqrt{25 (2)}$

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

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

Pull terms out from under the radical.

$x = \pm i \cdot (5 \sqrt{2})$

Move $5$ to the left of $i$ .

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

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.

$x = 5 i \sqrt{2}$

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

$x = - 5 i \sqrt{2}$

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

$x = 5 i \sqrt{2}, - 5 i \sqrt{2}$

Step 3

Find the Roots (Zeros) f(x)=-1/5x^2-10

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