Solve 1.05r^230=7.065

$$1.05 r ^ { 2 } 30 = 7.065$$

Solve for r

$$r=\frac{\sqrt{1099}}{70}\approx 0.473588127$$

$$r=-\frac{\sqrt{1099}}{70}\approx -0.473588127$$

Steps by Finding Square Root

Multiply 1.05 and 30 to get 31.5.

$$31.5r^{2}=7.065$$

Divide both sides by 31.5.

$$r^{2}=\frac{7.065}{31.5}$$

Expand \frac{7.065}{31.5} by multiplying both numerator and the denominator by 1000.

$$r^{2}=\frac{7065}{31500}$$

Reduce the fraction \frac{7065}{31500} to lowest terms by extracting and canceling out 45.

$$r^{2}=\frac{157}{700}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{1099}}{70} r=-\frac{\sqrt{1099}}{70}$$

Steps Using the Quadratic Formula

Multiply 1.05 and 30 to get 31.5.

$$31.5r^{2}=7.065$$

Subtract 7.065 from both sides.

$$31.5r^{2}-7.065=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 31.5 for a, 0 for b, and -7.065 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 31.5\left(-7.065\right)}}{2\times 31.5}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 31.5\left(-7.065\right)}}{2\times 31.5}$$

Multiply -4 times 31.5.

$$r=\frac{0±\sqrt{-126\left(-7.065\right)}}{2\times 31.5}$$

Multiply -126 times -7.065.

$$r=\frac{0±\sqrt{890.19}}{2\times 31.5}$$

Take the square root of 890.19.

$$r=\frac{0±\frac{9\sqrt{1099}}{10}}{2\times 31.5}$$

Multiply 2 times 31.5.

$$r=\frac{0±\frac{9\sqrt{1099}}{10}}{63}$$

Now solve the equation r=\frac{0±\frac{9\sqrt{1099}}{10}}{63} when ± is plus.

$$r=\frac{\sqrt{1099}}{70}$$

Now solve the equation r=\frac{0±\frac{9\sqrt{1099}}{10}}{63} when ± is minus.

$$r=-\frac{\sqrt{1099}}{70}$$

The equation is now solved.

$$r=\frac{\sqrt{1099}}{70} r=-\frac{\sqrt{1099}}{70}$$