Solve 105r^230=7065

$$105 r ^ { 2 } 30 = 7065$$

Solve for r

$$r = \frac{\sqrt{10990}}{70} \approx 1.497617155$$

$$r = -\frac{\sqrt{10990}}{70} \approx -1.497617155$$

Steps by Finding Square Root

Multiply 105 and 30 to get 3150.

$$3150r^{2}=7065$$

Divide both sides by 3150.

$$r^{2}=\frac{7065}{3150}$$

Reduce the fraction \frac{7065}{3150} to lowest terms by extracting and canceling out 45.

$$r^{2}=\frac{157}{70}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{10990}}{70} r=-\frac{\sqrt{10990}}{70}$$

Steps Using the Quadratic Formula

Multiply 105 and 30 to get 3150.

$$3150r^{2}=7065$$

Subtract 7065 from both sides.

$$3150r^{2}-7065=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3150 for a, 0 for b, and -7065 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 3150\left(-7065\right)}}{2\times 3150}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 3150\left(-7065\right)}}{2\times 3150}$$

Multiply -4 times 3150.

$$r=\frac{0±\sqrt{-12600\left(-7065\right)}}{2\times 3150}$$

Multiply -12600 times -7065.

$$r=\frac{0±\sqrt{89019000}}{2\times 3150}$$

Take the square root of 89019000.

$$r=\frac{0±90\sqrt{10990}}{2\times 3150}$$

Multiply 2 times 3150.

$$r=\frac{0±90\sqrt{10990}}{6300}$$

Now solve the equation r=\frac{0±90\sqrt{10990}}{6300} when ± is plus.

$$r=\frac{\sqrt{10990}}{70}$$

Now solve the equation r=\frac{0±90\sqrt{10990}}{6300} when ± is minus.

$$r=-\frac{\sqrt{10990}}{70}$$

The equation is now solved.

$$r=\frac{\sqrt{10990}}{70} r=-\frac{\sqrt{10990}}{70}$$