Solve 1200*x^2=1379.02

$$1200 \times x ^ { 2 } = 1379.02$$

Solve for x

$$x = \frac{19 \sqrt{1146}}{600} \approx 1.071999689$$

$$x = -\frac{19 \sqrt{1146}}{600} \approx -1.071999689$$

Steps by Finding Square Root

Divide both sides by 1200.

$$x^{2}=\frac{1379.02}{1200}$$

Expand \frac{1379.02}{1200} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{137902}{120000}$$

Reduce the fraction \frac{137902}{120000} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{68951}{60000}$$

Take the square root of both sides of the equation.

$$x=\frac{19\sqrt{1146}}{600} x=-\frac{19\sqrt{1146}}{600}$$

Steps Using the Quadratic Formula

Divide both sides by 1200.

$$x^{2}=\frac{1379.02}{1200}$$

Expand \frac{1379.02}{1200} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{137902}{120000}$$

Reduce the fraction \frac{137902}{120000} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{68951}{60000}$$

Subtract \frac{68951}{60000} from both sides.

$$x^{2}-\frac{68951}{60000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{68951}{60000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{68951}{60000}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{68951}{60000}\right)}}{2}$$

Multiply -4 times -\frac{68951}{60000}.

$$x=\frac{0±\sqrt{\frac{68951}{15000}}}{2}$$

Take the square root of \frac{68951}{15000}.

$$x=\frac{0±\frac{19\sqrt{1146}}{300}}{2}$$

Now solve the equation x=\frac{0±\frac{19\sqrt{1146}}{300}}{2} when ± is plus.

$$x=\frac{19\sqrt{1146}}{600}$$

Now solve the equation x=\frac{0±\frac{19\sqrt{1146}}{300}}{2} when ± is minus.

$$x=-\frac{19\sqrt{1146}}{600}$$

The equation is now solved.

$$x=\frac{19\sqrt{1146}}{600} x=-\frac{19\sqrt{1146}}{600}$$