Solve 11(16)(35)-11(r)^2(35)=16

$$11 ( 16 ) ( 35 ) - 11 ( r ) ^ { 2 } ( 35 ) = 16$$

Solve for r

$$r = \frac{32 \sqrt{2310}}{385} \approx 3.994801817$$

$$r = -\frac{32 \sqrt{2310}}{385} \approx -3.994801817$$

Steps by Finding Square Root

Multiply 11 and 16 to get 176.

$$176\times 35-11r^{2}\times 35=16$$

Multiply 176 and 35 to get 6160.

$$6160-11r^{2}\times 35=16$$

Multiply 11 and 35 to get 385.

$$6160-385r^{2}=16$$

Subtract 6160 from both sides.

$$-385r^{2}=16-6160$$

Subtract 6160 from 16 to get -6144.

$$-385r^{2}=-6144$$

Divide both sides by -385.

$$r^{2}=\frac{-6144}{-385}$$

Fraction \frac{-6144}{-385} can be simplified to \frac{6144}{385} by removing the negative sign from both the numerator and the denominator.

$$r^{2}=\frac{6144}{385}$$

Take the square root of both sides of the equation.

$$r=\frac{32\sqrt{2310}}{385} r=-\frac{32\sqrt{2310}}{385}$$

Steps Using the Quadratic Formula

Multiply 11 and 16 to get 176.

$$176\times 35-11r^{2}\times 35=16$$

Multiply 176 and 35 to get 6160.

$$6160-11r^{2}\times 35=16$$

Multiply 11 and 35 to get 385.

$$6160-385r^{2}=16$$

Subtract 16 from both sides.

$$6160-385r^{2}-16=0$$

Subtract 16 from 6160 to get 6144.

$$6144-385r^{2}=0$$

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.

$$-385r^{2}+6144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -385 for a, 0 for b, and 6144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-385\right)\times 6144}}{2\left(-385\right)}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-385\right)\times 6144}}{2\left(-385\right)}$$

Multiply -4 times -385.

$$r=\frac{0±\sqrt{1540\times 6144}}{2\left(-385\right)}$$

Multiply 1540 times 6144.

$$r=\frac{0±\sqrt{9461760}}{2\left(-385\right)}$$

Take the square root of 9461760.

$$r=\frac{0±64\sqrt{2310}}{2\left(-385\right)}$$

Multiply 2 times -385.

$$r=\frac{0±64\sqrt{2310}}{-770}$$

Now solve the equation r=\frac{0±64\sqrt{2310}}{-770} when ± is plus.

$$r=-\frac{32\sqrt{2310}}{385}$$

Now solve the equation r=\frac{0±64\sqrt{2310}}{-770} when ± is minus.

$$r=\frac{32\sqrt{2310}}{385}$$

The equation is now solved.

$$r=-\frac{32\sqrt{2310}}{385} r=\frac{32\sqrt{2310}}{385}$$