Solve (1-3)^2+(7/2+3)^2=r^2

$$( 1 - 3 ) ^ { 2 } + ( \frac { 7 } { 2 } + 3 ) ^ { 2 } = r ^ { 2 }$$

Solve for r

$$r = \frac{\sqrt{185}}{2} \approx 6.800735254$$

$$r = -\frac{\sqrt{185}}{2} \approx -6.800735254$$

Steps by Finding Square Root

Subtract 3 from 1 to get -2.

$$\left(-2\right)^{2}+\left(\frac{7}{2}+3\right)^{2}=r^{2}$$

Calculate -2 to the power of 2 and get 4.

$$4+\left(\frac{7}{2}+3\right)^{2}=r^{2}$$

Add \frac{7}{2} and 3 to get \frac{13}{2}.

$$4+\left(\frac{13}{2}\right)^{2}=r^{2}$$

Calculate \frac{13}{2} to the power of 2 and get \frac{169}{4}.

$$4+\frac{169}{4}=r^{2}$$

Add 4 and \frac{169}{4} to get \frac{185}{4}.

$$\frac{185}{4}=r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$r^{2}=\frac{185}{4}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{185}}{2} r=-\frac{\sqrt{185}}{2}$$

Steps Using the Quadratic Formula

Subtract 3 from 1 to get -2.

$$\left(-2\right)^{2}+\left(\frac{7}{2}+3\right)^{2}=r^{2}$$

Calculate -2 to the power of 2 and get 4.

$$4+\left(\frac{7}{2}+3\right)^{2}=r^{2}$$

Add \frac{7}{2} and 3 to get \frac{13}{2}.

$$4+\left(\frac{13}{2}\right)^{2}=r^{2}$$

Calculate \frac{13}{2} to the power of 2 and get \frac{169}{4}.

$$4+\frac{169}{4}=r^{2}$$

Add 4 and \frac{169}{4} to get \frac{185}{4}.

$$\frac{185}{4}=r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$r^{2}=\frac{185}{4}$$

Subtract \frac{185}{4} from both sides.

$$r^{2}-\frac{185}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{185}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{185}{4}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{185}{4}\right)}}{2}$$

Multiply -4 times -\frac{185}{4}.

$$r=\frac{0±\sqrt{185}}{2}$$

Now solve the equation r=\frac{0±\sqrt{185}}{2} when ± is plus.

$$r=\frac{\sqrt{185}}{2}$$

Now solve the equation r=\frac{0±\sqrt{185}}{2} when ± is minus.

$$r=-\frac{\sqrt{185}}{2}$$

The equation is now solved.

$$r=\frac{\sqrt{185}}{2} r=-\frac{\sqrt{185}}{2}$$