Solve 40-2qquadq=5

$$40 - 2 q \quad q = 5$$

Solve for q

$$q = \frac{\sqrt{70}}{2} \approx 4.183300133$$

$$q = -\frac{\sqrt{70}}{2} \approx -4.183300133$$

Steps by Finding Square Root

Multiply q and q to get q^{2}.

$$40-2q^{2}=5$$

Subtract 40 from both sides.

$$-2q^{2}=5-40$$

Subtract 40 from 5 to get -35.

$$-2q^{2}=-35$$

Divide both sides by -2.

$$q^{2}=\frac{-35}{-2}$$

Fraction \frac{-35}{-2} can be simplified to \frac{35}{2} by removing the negative sign from both the numerator and the denominator.

$$q^{2}=\frac{35}{2}$$

Take the square root of both sides of the equation.

$$q=\frac{\sqrt{70}}{2} q=-\frac{\sqrt{70}}{2}$$

Steps Using the Quadratic Formula

Multiply q and q to get q^{2}.

$$40-2q^{2}=5$$

Subtract 5 from both sides.

$$40-2q^{2}-5=0$$

Subtract 5 from 40 to get 35.

$$35-2q^{2}=0$$

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.

$$-2q^{2}+35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 35}}{2\left(-2\right)}$$

Square 0.

$$q=\frac{0±\sqrt{-4\left(-2\right)\times 35}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$q=\frac{0±\sqrt{8\times 35}}{2\left(-2\right)}$$

Multiply 8 times 35.

$$q=\frac{0±\sqrt{280}}{2\left(-2\right)}$$

Take the square root of 280.

$$q=\frac{0±2\sqrt{70}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$q=\frac{0±2\sqrt{70}}{-4}$$

Now solve the equation q=\frac{0±2\sqrt{70}}{-4} when ± is plus.

$$q=-\frac{\sqrt{70}}{2}$$

Now solve the equation q=\frac{0±2\sqrt{70}}{-4} when ± is minus.

$$q=\frac{\sqrt{70}}{2}$$

The equation is now solved.

$$q=-\frac{\sqrt{70}}{2} q=\frac{\sqrt{70}}{2}$$