Solve 18-t^2=0

$$18 - t ^ { 2 } = 0$$

Solve for t

$$t=3\sqrt{2}\approx 4.242640687$$

$$t=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$-t^{2}=-18$$

Divide both sides by -1.

$$t^{2}=\frac{-18}{-1}$$

Fraction \frac{-18}{-1} can be simplified to 18 by removing the negative sign from both the numerator and the denominator.

$$t^{2}=18$$

Take the square root of both sides of the equation.

$$t=3\sqrt{2} t=-3\sqrt{2}$$

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.

$$-t^{2}+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 18}}{2\left(-1\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-1\right)\times 18}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$t=\frac{0±\sqrt{4\times 18}}{2\left(-1\right)}$$

Multiply 4 times 18.

$$t=\frac{0±\sqrt{72}}{2\left(-1\right)}$$

Take the square root of 72.

$$t=\frac{0±6\sqrt{2}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$t=\frac{0±6\sqrt{2}}{-2}$$

Now solve the equation t=\frac{0±6\sqrt{2}}{-2} when ± is plus.

$$t=-3\sqrt{2}$$

Now solve the equation t=\frac{0±6\sqrt{2}}{-2} when ± is minus.

$$t=3\sqrt{2}$$

The equation is now solved.

$$t=-3\sqrt{2} t=3\sqrt{2}$$