Solve 1/2*9.8/6*x^2=100

$$\frac{ 1 }{ 2 } \times \frac{ 9.8 }{ 6 } \times { x }^{ 2 } =100$$

Solve for x

$$x = \frac{20 \sqrt{15}}{7} \approx 11.065666703$$

$$x = -\frac{20 \sqrt{15}}{7} \approx -11.065666703$$

Steps by Finding Square Root

Expand \frac{9.8}{6} by multiplying both numerator and the denominator by 10.

$$\frac{1}{2}\times \frac{98}{60}x^{2}=100$$

Reduce the fraction \frac{98}{60} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{49}{30}x^{2}=100$$

Multiply \frac{1}{2} and \frac{49}{30} to get \frac{49}{60}.

$$\frac{49}{60}x^{2}=100$$

Multiply both sides by \frac{60}{49}, the reciprocal of \frac{49}{60}.

$$x^{2}=100\times \frac{60}{49}$$

Multiply 100 and \frac{60}{49} to get \frac{6000}{49}.

$$x^{2}=\frac{6000}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{20\sqrt{15}}{7} x=-\frac{20\sqrt{15}}{7}$$

Steps Using the Quadratic Formula

Expand \frac{9.8}{6} by multiplying both numerator and the denominator by 10.

$$\frac{1}{2}\times \frac{98}{60}x^{2}=100$$

Reduce the fraction \frac{98}{60} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{49}{30}x^{2}=100$$

Multiply \frac{1}{2} and \frac{49}{30} to get \frac{49}{60}.

$$\frac{49}{60}x^{2}=100$$

Subtract 100 from both sides.

$$\frac{49}{60}x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{60} for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{49}{60}\left(-100\right)}}{2\times \frac{49}{60}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{49}{60}\left(-100\right)}}{2\times \frac{49}{60}}$$

Multiply -4 times \frac{49}{60}.

$$x=\frac{0±\sqrt{-\frac{49}{15}\left(-100\right)}}{2\times \frac{49}{60}}$$

Multiply -\frac{49}{15} times -100.

$$x=\frac{0±\sqrt{\frac{980}{3}}}{2\times \frac{49}{60}}$$

Take the square root of \frac{980}{3}.

$$x=\frac{0±\frac{14\sqrt{15}}{3}}{2\times \frac{49}{60}}$$

Multiply 2 times \frac{49}{60}.

$$x=\frac{0±\frac{14\sqrt{15}}{3}}{\frac{49}{30}}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{15}}{3}}{\frac{49}{30}} when ± is plus.

$$x=\frac{20\sqrt{15}}{7}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{15}}{3}}{\frac{49}{30}} when ± is minus.

$$x=-\frac{20\sqrt{15}}{7}$$

The equation is now solved.

$$x=\frac{20\sqrt{15}}{7} x=-\frac{20\sqrt{15}}{7}$$