Solve 27.952++4.9t^2-60=0

$$27.952 + + 4.9 t ^ { 2 } - 60 = 0$$

Solve for t

$$t = \frac{2 \sqrt{2003}}{35} \approx 2.557422171$$

$$t = -\frac{2 \sqrt{2003}}{35} \approx -2.557422171$$

Steps by Finding Square Root

Subtract 60 from 27.952 to get -32.048.

$$-32.048+4.9t^{2}=0$$

Add 32.048 to both sides. Anything plus zero gives itself.

$$4.9t^{2}=32.048$$

Divide both sides by 4.9.

$$t^{2}=\frac{32.048}{4.9}$$

Expand \frac{32.048}{4.9} by multiplying both numerator and the denominator by 1000.

$$t^{2}=\frac{32048}{4900}$$

Reduce the fraction \frac{32048}{4900} to lowest terms by extracting and canceling out 4.

$$t^{2}=\frac{8012}{1225}$$

Take the square root of both sides of the equation.

$$t=\frac{2\sqrt{2003}}{35} t=-\frac{2\sqrt{2003}}{35}$$

Steps Using the Quadratic Formula

Subtract 60 from 27.952 to get -32.048.

$$-32.048+4.9t^{2}=0$$

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.

$$4.9t^{2}-32.048=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4.9 for a, 0 for b, and -32.048 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 4.9\left(-32.048\right)}}{2\times 4.9}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 4.9\left(-32.048\right)}}{2\times 4.9}$$

Multiply -4 times 4.9.

$$t=\frac{0±\sqrt{-19.6\left(-32.048\right)}}{2\times 4.9}$$

Multiply -19.6 times -32.048 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$t=\frac{0±\sqrt{628.1408}}{2\times 4.9}$$

Take the square root of 628.1408.

$$t=\frac{0±\frac{14\sqrt{2003}}{25}}{2\times 4.9}$$

Multiply 2 times 4.9.

$$t=\frac{0±\frac{14\sqrt{2003}}{25}}{9.8}$$

Now solve the equation t=\frac{0±\frac{14\sqrt{2003}}{25}}{9.8} when ± is plus.

$$t=\frac{2\sqrt{2003}}{35}$$

Now solve the equation t=\frac{0±\frac{14\sqrt{2003}}{25}}{9.8} when ± is minus.

$$t=-\frac{2\sqrt{2003}}{35}$$

The equation is now solved.

$$t=\frac{2\sqrt{2003}}{35} t=-\frac{2\sqrt{2003}}{35}$$