Solve 7000(1-x^2)=5670

$$7000 ( 1 - x ^ { 2 } ) = 5670$$

Solve for x

$$x=\frac{\sqrt{19}}{10}\approx 0.435889894$$

$$x=-\frac{\sqrt{19}}{10}\approx -0.435889894$$

Steps by Finding Square Root

Divide both sides by 7000.

$$1-x^{2}=\frac{5670}{7000}$$

Reduce the fraction \frac{5670}{7000} to lowest terms by extracting and canceling out 70.

$$1-x^{2}=\frac{81}{100}$$

Subtract 1 from both sides.

$$-x^{2}=\frac{81}{100}-1$$

Subtract 1 from \frac{81}{100} to get -\frac{19}{100}.

$$-x^{2}=-\frac{19}{100}$$

Divide both sides by -1.

$$x^{2}=\frac{-\frac{19}{100}}{-1}$$

Express \frac{-\frac{19}{100}}{-1} as a single fraction.

$$x^{2}=\frac{-19}{100\left(-1\right)}$$

Multiply 100 and -1 to get -100.

$$x^{2}=\frac{-19}{-100}$$

Fraction \frac{-19}{-100} can be simplified to \frac{19}{100} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{19}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{19}}{10} x=-\frac{\sqrt{19}}{10}$$

Steps Using the Quadratic Formula

Divide both sides by 7000.

$$1-x^{2}=\frac{5670}{7000}$$

Reduce the fraction \frac{5670}{7000} to lowest terms by extracting and canceling out 70.

$$1-x^{2}=\frac{81}{100}$$

Subtract \frac{81}{100} from both sides.

$$1-x^{2}-\frac{81}{100}=0$$

Subtract \frac{81}{100} from 1 to get \frac{19}{100}.

$$\frac{19}{100}-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}+\frac{19}{100}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and \frac{19}{100} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times \frac{19}{100}}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times \frac{19}{100}}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times \frac{19}{100}}}{2\left(-1\right)}$$

Multiply 4 times \frac{19}{100}.

$$x=\frac{0±\sqrt{\frac{19}{25}}}{2\left(-1\right)}$$

Take the square root of \frac{19}{25}.

$$x=\frac{0±\frac{\sqrt{19}}{5}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\frac{\sqrt{19}}{5}}{-2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{19}}{5}}{-2} when ± is plus.

$$x=-\frac{\sqrt{19}}{10}$$

Now solve the equation x=\frac{0±\frac{\sqrt{19}}{5}}{-2} when ± is minus.

$$x=\frac{\sqrt{19}}{10}$$

The equation is now solved.

$$x=-\frac{\sqrt{19}}{10} x=\frac{\sqrt{19}}{10}$$