Solve 81-1/25x^2=0

$$81 - \frac { 1 } { 25 } x ^ { 2 } = 0$$

Solve for x

$$x=45$$

$$x=-45$$

Steps by Finding Square Root

Subtract 81 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{25}x^{2}=-81$$

Multiply both sides by -25, the reciprocal of -\frac{1}{25}.

$$x^{2}=-81\left(-25\right)$$

Multiply -81 and -25 to get 2025.

$$x^{2}=2025$$

Take the square root of both sides of the equation.

$$x=45 x=-45$$

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.

$$-\frac{1}{25}x^{2}+81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{25} for a, 0 for b, and 81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{25}\right)\times 81}}{2\left(-\frac{1}{25}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{25}\right)\times 81}}{2\left(-\frac{1}{25}\right)}$$

Multiply -4 times -\frac{1}{25}.

$$x=\frac{0±\sqrt{\frac{4}{25}\times 81}}{2\left(-\frac{1}{25}\right)}$$

Multiply \frac{4}{25} times 81.

$$x=\frac{0±\sqrt{\frac{324}{25}}}{2\left(-\frac{1}{25}\right)}$$

Take the square root of \frac{324}{25}.

$$x=\frac{0±\frac{18}{5}}{2\left(-\frac{1}{25}\right)}$$

Multiply 2 times -\frac{1}{25}.

$$x=\frac{0±\frac{18}{5}}{-\frac{2}{25}}$$

Now solve the equation x=\frac{0±\frac{18}{5}}{-\frac{2}{25}} when ± is plus.

$$x=-45$$

Now solve the equation x=\frac{0±\frac{18}{5}}{-\frac{2}{25}} when ± is minus.

$$x=45$$

The equation is now solved.

$$x=-45 x=45$$