Solve 81-64/3-x^2/frac{64{3}}=1/2

$$\frac { 81 - \frac { 64 } { 3 } - x ^ { 2 } } { \frac { 64 } { 3 } } = \frac { 1 } { 2 }$$

Solve for x

$$x=7$$

$$x=-7$$

Steps by Finding Square Root

Multiply both sides by \frac{64}{3}.

$$81-\frac{64}{3}-x^{2}=\frac{1}{2}\times \frac{64}{3}$$

Subtract \frac{64}{3} from 81 to get \frac{179}{3}.

$$\frac{179}{3}-x^{2}=\frac{1}{2}\times \frac{64}{3}$$

Multiply \frac{1}{2} and \frac{64}{3} to get \frac{32}{3}.

$$\frac{179}{3}-x^{2}=\frac{32}{3}$$

Subtract \frac{179}{3} from both sides.

$$-x^{2}=\frac{32}{3}-\frac{179}{3}$$

Subtract \frac{179}{3} from \frac{32}{3} to get -49.

$$-x^{2}=-49$$

Divide both sides by -1.

$$x^{2}=\frac{-49}{-1}$$

Fraction \frac{-49}{-1} can be simplified to 49 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=49$$

Take the square root of both sides of the equation.

$$x=7 x=-7$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{64}{3}.

$$81-\frac{64}{3}-x^{2}=\frac{1}{2}\times \frac{64}{3}$$

Subtract \frac{64}{3} from 81 to get \frac{179}{3}.

$$\frac{179}{3}-x^{2}=\frac{1}{2}\times \frac{64}{3}$$

Multiply \frac{1}{2} and \frac{64}{3} to get \frac{32}{3}.

$$\frac{179}{3}-x^{2}=\frac{32}{3}$$

Subtract \frac{32}{3} from both sides.

$$\frac{179}{3}-x^{2}-\frac{32}{3}=0$$

Subtract \frac{32}{3} from \frac{179}{3} to get 49.

$$49-x^{2}=0$$

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.

$$-x^{2}+49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 49}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 49}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 49}}{2\left(-1\right)}$$

Multiply 4 times 49.

$$x=\frac{0±\sqrt{196}}{2\left(-1\right)}$$

Take the square root of 196.

$$x=\frac{0±14}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±14}{-2}$$

Now solve the equation x=\frac{0±14}{-2} when ± is plus. Divide 14 by -2.

$$x=-7$$

Now solve the equation x=\frac{0±14}{-2} when ± is minus. Divide -14 by -2.

$$x=7$$

The equation is now solved.

$$x=-7 x=7$$