Solve 0.5^2+1.2^2=c^2

$$0.5 ^ { 2 } + 1.2 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=1.3$$

$$c=-1.3$$

Steps Using Difference of Squares

Calculate 0.5 to the power of 2 and get 0.25.

$$0.25+1.2^{2}=c^{2}$$

Calculate 1.2 to the power of 2 and get 1.44.

$$0.25+1.44=c^{2}$$

Add 0.25 and 1.44 to get 1.69.

$$1.69=c^{2}$$

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

$$c^{2}=1.69$$

Subtract 1.69 from both sides.

$$c^{2}-1.69=0$$

Consider c^{2}-1.69. Rewrite c^{2}-1.69 as c^{2}-\left(\frac{13}{10}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-\frac{13}{10}\right)\left(c+\frac{13}{10}\right)=0$$

To find equation solutions, solve c-\frac{13}{10}=0 and c+\frac{13}{10}=0.

$$c=\frac{13}{10} c=-\frac{13}{10}$$

Steps by Finding Square Root

Calculate 0.5 to the power of 2 and get 0.25.

$$0.25+1.2^{2}=c^{2}$$

Calculate 1.2 to the power of 2 and get 1.44.

$$0.25+1.44=c^{2}$$

Add 0.25 and 1.44 to get 1.69.

$$1.69=c^{2}$$

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

$$c^{2}=1.69$$

Take the square root of both sides of the equation.

$$c=\frac{13}{10} c=-\frac{13}{10}$$

Steps Using the Quadratic Formula

Calculate 0.5 to the power of 2 and get 0.25.

$$0.25+1.2^{2}=c^{2}$$

Calculate 1.2 to the power of 2 and get 1.44.

$$0.25+1.44=c^{2}$$

Add 0.25 and 1.44 to get 1.69.

$$1.69=c^{2}$$

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

$$c^{2}=1.69$$

Subtract 1.69 from both sides.

$$c^{2}-1.69=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1.69 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1.69\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1.69\right)}}{2}$$

Multiply -4 times -1.69.

$$c=\frac{0±\sqrt{6.76}}{2}$$

Take the square root of 6.76.

$$c=\frac{0±\frac{13}{5}}{2}$$

Now solve the equation c=\frac{0±\frac{13}{5}}{2} when ± is plus.

$$c=\frac{13}{10}$$

Now solve the equation c=\frac{0±\frac{13}{5}}{2} when ± is minus.

$$c=-\frac{13}{10}$$

The equation is now solved.

$$c=\frac{13}{10} c=-\frac{13}{10}$$