Solve 1/2=25+64-x^2/80

$$\frac { 1 } { 2 } = \frac { 25 + 64 - x ^ { 2 } } { 80 }$$

Solve for x

$$x=7$$

$$x=-7$$

Steps by Finding Square Root

Multiply both sides by 80.

$$\frac{1}{2}\times 80=25+64-x^{2}$$

Multiply \frac{1}{2} and 80 to get 40.

$$40=25+64-x^{2}$$

Add 25 and 64 to get 89.

$$40=89-x^{2}$$

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

$$89-x^{2}=40$$

Subtract 89 from both sides.

$$-x^{2}=40-89$$

Subtract 89 from 40 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 80.

$$\frac{1}{2}\times 80=25+64-x^{2}$$

Multiply \frac{1}{2} and 80 to get 40.

$$40=25+64-x^{2}$$

Add 25 and 64 to get 89.

$$40=89-x^{2}$$

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

$$89-x^{2}=40$$

Subtract 40 from both sides.

$$89-x^{2}-40=0$$

Subtract 40 from 89 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.

$$x=-7 x=7$$