Solve 7^2+2^2=c^2

$$7 ^ { 2 } + 2 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{53}\approx 7.280109889$$

$$c=-\sqrt{53}\approx -7.280109889$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$49+2^{2}=c^{2}$$

Calculate 2 to the power of 2 and get 4.

$$49+4=c^{2}$$

Add 49 and 4 to get 53.

$$53=c^{2}$$

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

$$c^{2}=53$$

Take the square root of both sides of the equation.

$$c=\sqrt{53} c=-\sqrt{53}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$49+2^{2}=c^{2}$$

Calculate 2 to the power of 2 and get 4.

$$49+4=c^{2}$$

Add 49 and 4 to get 53.

$$53=c^{2}$$

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

$$c^{2}=53$$

Subtract 53 from both sides.

$$c^{2}-53=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -53 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-53\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-53\right)}}{2}$$

Multiply -4 times -53.

$$c=\frac{0±\sqrt{212}}{2}$$

Take the square root of 212.

$$c=\frac{0±2\sqrt{53}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{53}}{2} when ± is plus.

$$c=\sqrt{53}$$

Now solve the equation c=\frac{0±2\sqrt{53}}{2} when ± is minus.

$$c=-\sqrt{53}$$

The equation is now solved.

$$c=\sqrt{53} c=-\sqrt{53}$$