Solve 15-0.050=-Q^2/40+150+25/2

$$15 - 0.050 = \frac { - Q ^ { 2 } } { 40 } + 150 + \frac { 25 } { 2 }$$

Solve for Q

$$Q=\sqrt{5902}\approx 76.824475267$$

$$Q=-\sqrt{5902}\approx -76.824475267$$

Steps by Finding Square Root

Multiply both sides of the equation by 40, the least common multiple of 40,2.

$$600-2=-Q^{2}+6000+500$$

Subtract 2 from 600 to get 598.

$$598=-Q^{2}+6000+500$$

Add 6000 and 500 to get 6500.

$$598=-Q^{2}+6500$$

Swap sides so that all variable terms are on the left hand side.

$$-Q^{2}+6500=598$$

Subtract 6500 from both sides.

$$-Q^{2}=598-6500$$

Subtract 6500 from 598 to get -5902.

$$-Q^{2}=-5902$$

Divide both sides by -1.

$$Q^{2}=\frac{-5902}{-1}$$

Fraction \frac{-5902}{-1} can be simplified to 5902 by removing the negative sign from both the numerator and the denominator.

$$Q^{2}=5902$$

Take the square root of both sides of the equation.

$$Q=\sqrt{5902} Q=-\sqrt{5902}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 40, the least common multiple of 40,2.

$$600-2=-Q^{2}+6000+500$$

Subtract 2 from 600 to get 598.

$$598=-Q^{2}+6000+500$$

Add 6000 and 500 to get 6500.

$$598=-Q^{2}+6500$$

Swap sides so that all variable terms are on the left hand side.

$$-Q^{2}+6500=598$$

Subtract 598 from both sides.

$$-Q^{2}+6500-598=0$$

Subtract 598 from 6500 to get 5902.

$$-Q^{2}+5902=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 5902 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$Q=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 5902}}{2\left(-1\right)}$$

Square 0.

$$Q=\frac{0±\sqrt{-4\left(-1\right)\times 5902}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$Q=\frac{0±\sqrt{4\times 5902}}{2\left(-1\right)}$$

Multiply 4 times 5902.

$$Q=\frac{0±\sqrt{23608}}{2\left(-1\right)}$$

Take the square root of 23608.

$$Q=\frac{0±2\sqrt{5902}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$Q=\frac{0±2\sqrt{5902}}{-2}$$

Now solve the equation Q=\frac{0±2\sqrt{5902}}{-2} when ± is plus.

$$Q=-\sqrt{5902}$$

Now solve the equation Q=\frac{0±2\sqrt{5902}}{-2} when ± is minus.

$$Q=\sqrt{5902}$$

The equation is now solved.

$$Q=-\sqrt{5902} Q=\sqrt{5902}$$