Solve 10=1/2*9.8x^2

$$10 = \frac { 1 } { 2 } \times 9.8 x ^ { 2 }$$

Solve for x

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

$$x = -\frac{10}{7} = -1\frac{3}{7} \approx -1.428571429$$

Steps Using Difference of Squares

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$10=\frac{49}{10}x^{2}$$

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

$$\frac{49}{10}x^{2}=10$$

Subtract 10 from both sides.

$$\frac{49}{10}x^{2}-10=0$$

Multiply both sides by 10.

$$49x^{2}-100=0$$

Consider 49x^{2}-100. Rewrite 49x^{2}-100 as \left(7x\right)^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7x-10\right)\left(7x+10\right)=0$$

To find equation solutions, solve 7x-10=0 and 7x+10=0.

$$x=\frac{10}{7} x=-\frac{10}{7}$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$10=\frac{49}{10}x^{2}$$

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

$$\frac{49}{10}x^{2}=10$$

Multiply both sides by \frac{10}{49}, the reciprocal of \frac{49}{10}.

$$x^{2}=10\times \frac{10}{49}$$

Multiply 10 and \frac{10}{49} to get \frac{100}{49}.

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

Take the square root of both sides of the equation.

$$x=\frac{10}{7} x=-\frac{10}{7}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$10=\frac{49}{10}x^{2}$$

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

$$\frac{49}{10}x^{2}=10$$

Subtract 10 from both sides.

$$\frac{49}{10}x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{10} for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-10\right)}}{2\times \frac{49}{10}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-10\right)}}{2\times \frac{49}{10}}$$

Multiply -4 times \frac{49}{10}.

$$x=\frac{0±\sqrt{-\frac{98}{5}\left(-10\right)}}{2\times \frac{49}{10}}$$

Multiply -\frac{98}{5} times -10.

$$x=\frac{0±\sqrt{196}}{2\times \frac{49}{10}}$$

Take the square root of 196.

$$x=\frac{0±14}{2\times \frac{49}{10}}$$

Multiply 2 times \frac{49}{10}.

$$x=\frac{0±14}{\frac{49}{5}}$$

Now solve the equation x=\frac{0±14}{\frac{49}{5}} when ± is plus. Divide 14 by \frac{49}{5} by multiplying 14 by the reciprocal of \frac{49}{5}.

$$x=\frac{10}{7}$$

Now solve the equation x=\frac{0±14}{\frac{49}{5}} when ± is minus. Divide -14 by \frac{49}{5} by multiplying -14 by the reciprocal of \frac{49}{5}.

$$x=-\frac{10}{7}$$

The equation is now solved.

$$x=\frac{10}{7} x=-\frac{10}{7}$$