Solve 94-4q^2=0

$$94 - 4 q ^ { 2 } = 0$$

Solve for q

$$q = \frac{\sqrt{94}}{2} \approx 4.847679857$$

$$q = -\frac{\sqrt{94}}{2} \approx -4.847679857$$

Steps by Finding Square Root

Subtract 94 from both sides. Anything subtracted from zero gives its negation.

$$-4q^{2}=-94$$

Divide both sides by -4.

$$q^{2}=\frac{-94}{-4}$$

Reduce the fraction \frac{-94}{-4} to lowest terms by extracting and canceling out -2.

$$q^{2}=\frac{47}{2}$$

Take the square root of both sides of the equation.

$$q=\frac{\sqrt{94}}{2} q=-\frac{\sqrt{94}}{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-4q^{2}+94=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 94 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 94}}{2\left(-4\right)}$$

Square 0.

$$q=\frac{0±\sqrt{-4\left(-4\right)\times 94}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$q=\frac{0±\sqrt{16\times 94}}{2\left(-4\right)}$$

Multiply 16 times 94.

$$q=\frac{0±\sqrt{1504}}{2\left(-4\right)}$$

Take the square root of 1504.

$$q=\frac{0±4\sqrt{94}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$q=\frac{0±4\sqrt{94}}{-8}$$

Now solve the equation q=\frac{0±4\sqrt{94}}{-8} when ± is plus.

$$q=-\frac{\sqrt{94}}{2}$$

Now solve the equation q=\frac{0±4\sqrt{94}}{-8} when ± is minus.

$$q=\frac{\sqrt{94}}{2}$$

The equation is now solved.

$$q=-\frac{\sqrt{94}}{2} q=\frac{\sqrt{94}}{2}$$