Solve 4.5^2+4.5^2=c^2

$$4.5 ^ { 2 } + 4.5 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c = \frac{9 \sqrt{2}}{2} \approx 6.363961031$$

$$c = -\frac{9 \sqrt{2}}{2} \approx -6.363961031$$

Steps by Finding Square Root

Calculate 4.5 to the power of 2 and get 20.25.

$$20.25+4.5^{2}=c^{2}$$

Calculate 4.5 to the power of 2 and get 20.25.

$$20.25+20.25=c^{2}$$

Add 20.25 and 20.25 to get 40.5.

$$40.5=c^{2}$$

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

$$c^{2}=40.5$$

Take the square root of both sides of the equation.

$$c=\frac{9\sqrt{2}}{2} c=-\frac{9\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Calculate 4.5 to the power of 2 and get 20.25.

$$20.25+4.5^{2}=c^{2}$$

Calculate 4.5 to the power of 2 and get 20.25.

$$20.25+20.25=c^{2}$$

Add 20.25 and 20.25 to get 40.5.

$$40.5=c^{2}$$

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

$$c^{2}=40.5$$

Subtract 40.5 from both sides.

$$c^{2}-40.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -40.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-40.5\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-40.5\right)}}{2}$$

Multiply -4 times -40.5.

$$c=\frac{0±\sqrt{162}}{2}$$

Take the square root of 162.

$$c=\frac{0±9\sqrt{2}}{2}$$

Now solve the equation c=\frac{0±9\sqrt{2}}{2} when ± is plus.

$$c=\frac{9\sqrt{2}}{2}$$

Now solve the equation c=\frac{0±9\sqrt{2}}{2} when ± is minus.

$$c=-\frac{9\sqrt{2}}{2}$$

The equation is now solved.

$$c=\frac{9\sqrt{2}}{2} c=-\frac{9\sqrt{2}}{2}$$