Solve 0.5*64.9*x^2=312.2*9.8*0.034

$$0.5 \times 64.9 \cdot x ^ { 2 } = 312.2 \times 9.8 \times 0.034$$

Solve for x

$$x = \frac{7 \sqrt{17222513}}{16225} \approx 1.790447517$$

$$x = -\frac{7 \sqrt{17222513}}{16225} \approx -1.790447517$$

Steps by Finding Square Root

Multiply 0.5 and 64.9 to get 32.45.

$$32.45x^{2}=312.2\times 9.8\times 0.034$$

Multiply 312.2 and 9.8 to get 3059.56.

$$32.45x^{2}=3059.56\times 0.034$$

Multiply 3059.56 and 0.034 to get 104.02504.

$$32.45x^{2}=104.02504$$

Divide both sides by 32.45.

$$x^{2}=\frac{104.02504}{32.45}$$

Expand \frac{104.02504}{32.45} by multiplying both numerator and the denominator by 100000.

$$x^{2}=\frac{10402504}{3245000}$$

Reduce the fraction \frac{10402504}{3245000} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{1300313}{405625}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{17222513}}{16225} x=-\frac{7\sqrt{17222513}}{16225}$$

Steps Using the Quadratic Formula

Multiply 0.5 and 64.9 to get 32.45.

$$32.45x^{2}=312.2\times 9.8\times 0.034$$

Multiply 312.2 and 9.8 to get 3059.56.

$$32.45x^{2}=3059.56\times 0.034$$

Multiply 3059.56 and 0.034 to get 104.02504.

$$32.45x^{2}=104.02504$$

Subtract 104.02504 from both sides.

$$32.45x^{2}-104.02504=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 32.45 for a, 0 for b, and -104.02504 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 32.45\left(-104.02504\right)}}{2\times 32.45}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 32.45\left(-104.02504\right)}}{2\times 32.45}$$

Multiply -4 times 32.45.

$$x=\frac{0±\sqrt{-129.8\left(-104.02504\right)}}{2\times 32.45}$$

Multiply -129.8 times -104.02504 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{13502.450192}}{2\times 32.45}$$

Take the square root of 13502.450192.

$$x=\frac{0±\frac{7\sqrt{17222513}}{250}}{2\times 32.45}$$

Multiply 2 times 32.45.

$$x=\frac{0±\frac{7\sqrt{17222513}}{250}}{64.9}$$

Now solve the equation x=\frac{0±\frac{7\sqrt{17222513}}{250}}{64.9} when ± is plus.

$$x=\frac{7\sqrt{17222513}}{16225}$$

Now solve the equation x=\frac{0±\frac{7\sqrt{17222513}}{250}}{64.9} when ± is minus.

$$x=-\frac{7\sqrt{17222513}}{16225}$$

The equation is now solved.

$$x=\frac{7\sqrt{17222513}}{16225} x=-\frac{7\sqrt{17222513}}{16225}$$