Solve -q^2=-65

$$- { q }^{ 2 } = -65$$

Solve for q

$$q=\sqrt{65}\approx 8.062257748$$

$$q=-\sqrt{65}\approx -8.062257748$$

Steps by Finding Square Root

Divide both sides by -1.

$$q^{2}=\frac{-65}{-1}$$

Fraction \frac{-65}{-1} can be simplified to 65 by removing the negative sign from both the numerator and the denominator.

$$q^{2}=65$$

Take the square root of both sides of the equation.

$$q=\sqrt{65} q=-\sqrt{65}$$

Steps Using the Quadratic Formula

Add 65 to both sides.

$$-q^{2}+65=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 65 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 65}}{2\left(-1\right)}$$

Square 0.

$$q=\frac{0±\sqrt{-4\left(-1\right)\times 65}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$q=\frac{0±\sqrt{4\times 65}}{2\left(-1\right)}$$

Multiply 4 times 65.

$$q=\frac{0±\sqrt{260}}{2\left(-1\right)}$$

Take the square root of 260.

$$q=\frac{0±2\sqrt{65}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$q=\frac{0±2\sqrt{65}}{-2}$$

Now solve the equation q=\frac{0±2\sqrt{65}}{-2} when ± is plus.

$$q=-\sqrt{65}$$

Now solve the equation q=\frac{0±2\sqrt{65}}{-2} when ± is minus.

$$q=\sqrt{65}$$

The equation is now solved.

$$q=-\sqrt{65} q=\sqrt{65}$$