Solve 0.643xquad0.766x/9.8=10.97

$$0.643 x \quad \frac { 0.766 x } { 9.8 } = 10.97$$

Solve for x

$$x = \frac{70 \sqrt{2701570930}}{246269} \approx 14.773945083$$

$$x = -\frac{70 \sqrt{2701570930}}{246269} \approx -14.773945083$$

Steps by Finding Square Root

Divide 0.766x by 9.8 to get \frac{383}{4900}x.

$$0.643x\times \frac{383}{4900}x=10.97$$

Multiply 0.643 and \frac{383}{4900} to get \frac{246269}{4900000}.

$$\frac{246269}{4900000}xx=10.97$$

Multiply x and x to get x^{2}.

$$\frac{246269}{4900000}x^{2}=10.97$$

Divide both sides by \frac{246269}{4900000}.

$$x^{2}=\frac{10.97}{\frac{246269}{4900000}}$$

Take the square root of both sides of the equation.

$$x=\frac{70\sqrt{2701570930}}{246269} x=-\frac{70\sqrt{2701570930}}{246269}$$

Steps Using the Quadratic Formula

Divide 0.766x by 9.8 to get \frac{383}{4900}x.

$$0.643x\times \frac{383}{4900}x=10.97$$

Multiply 0.643 and \frac{383}{4900} to get \frac{246269}{4900000}.

$$\frac{246269}{4900000}xx=10.97$$

Multiply x and x to get x^{2}.

$$\frac{246269}{4900000}x^{2}=10.97$$

Subtract 10.97 from both sides.

$$\frac{246269}{4900000}x^{2}-10.97=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{246269}{4900000} for a, 0 for b, and -10.97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{246269}{4900000}\left(-10.97\right)}}{2\times \frac{246269}{4900000}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{246269}{4900000}\left(-10.97\right)}}{2\times \frac{246269}{4900000}}$$

Multiply -4 times \frac{246269}{4900000}.

$$x=\frac{0±\sqrt{-\frac{246269}{1225000}\left(-10.97\right)}}{2\times \frac{246269}{4900000}}$$

Multiply -\frac{246269}{1225000} times -10.97 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{270157093}{122500000}}}{2\times \frac{246269}{4900000}}$$

Take the square root of \frac{270157093}{122500000}.

$$x=\frac{0±\frac{\sqrt{2701570930}}{35000}}{2\times \frac{246269}{4900000}}$$

Multiply 2 times \frac{246269}{4900000}.

$$x=\frac{0±\frac{\sqrt{2701570930}}{35000}}{\frac{246269}{2450000}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{2701570930}}{35000}}{\frac{246269}{2450000}} when ± is plus.

$$x=\frac{70\sqrt{2701570930}}{246269}$$

Now solve the equation x=\frac{0±\frac{\sqrt{2701570930}}{35000}}{\frac{246269}{2450000}} when ± is minus.

$$x=-\frac{70\sqrt{2701570930}}{246269}$$

The equation is now solved.

$$x=\frac{70\sqrt{2701570930}}{246269} x=-\frac{70\sqrt{2701570930}}{246269}$$