Solve 36=0+-4.9t^2

$$36 = 0+-4.9 { t }^{ 2 }$$

Solve for t

$$t=-\frac{i\times 6\sqrt{10}}{7}\approx -0-2.710523709i$$

$$t=\frac{i\times 6\sqrt{10}}{7}\approx 2.710523709i$$

Steps by Finding Square Root

Anything plus zero gives itself.

$$36=-4.9t^{2}$$

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

$$-4.9t^{2}=36$$

Divide both sides by -4.9.

$$t^{2}=\frac{36}{-4.9}$$

Expand \frac{36}{-4.9} by multiplying both numerator and the denominator by 10.

$$t^{2}=\frac{360}{-49}$$

Fraction \frac{360}{-49} can be rewritten as -\frac{360}{49} by extracting the negative sign.

$$t^{2}=-\frac{360}{49}$$

The equation is now solved.

$$t=\frac{6\sqrt{10}i}{7} t=-\frac{6\sqrt{10}i}{7}$$

Steps Using the Quadratic Formula

Anything plus zero gives itself.

$$36=-4.9t^{2}$$

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

$$-4.9t^{2}=36$$

Subtract 36 from both sides.

$$-4.9t^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4.9 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-4.9\right)\left(-36\right)}}{2\left(-4.9\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-4.9\right)\left(-36\right)}}{2\left(-4.9\right)}$$

Multiply -4 times -4.9.

$$t=\frac{0±\sqrt{19.6\left(-36\right)}}{2\left(-4.9\right)}$$

Multiply 19.6 times -36.

$$t=\frac{0±\sqrt{-705.6}}{2\left(-4.9\right)}$$

Take the square root of -705.6.

$$t=\frac{0±\frac{42\sqrt{10}i}{5}}{2\left(-4.9\right)}$$

Multiply 2 times -4.9.

$$t=\frac{0±\frac{42\sqrt{10}i}{5}}{-9.8}$$

Now solve the equation t=\frac{0±\frac{42\sqrt{10}i}{5}}{-9.8} when ± is plus.

$$t=-\frac{6\sqrt{10}i}{7}$$

Now solve the equation t=\frac{0±\frac{42\sqrt{10}i}{5}}{-9.8} when ± is minus.

$$t=\frac{6\sqrt{10}i}{7}$$

The equation is now solved.

$$t=-\frac{6\sqrt{10}i}{7} t=\frac{6\sqrt{10}i}{7}$$