Solve 7.2^2+9.6^2=x^2

$${ 7.2 }^{ 2 } + { 9.6 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x=12$$

$$x=-12$$

Steps Using Difference of Squares

Calculate 7.2 to the power of 2 and get 51.84.

$$51.84+9.6^{2}=x^{2}$$

Calculate 9.6 to the power of 2 and get 92.16.

$$51.84+92.16=x^{2}$$

Add 51.84 and 92.16 to get 144.

$$144=x^{2}$$

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

$$x^{2}=144$$

Subtract 144 from both sides.

$$x^{2}-144=0$$

Consider x^{2}-144. Rewrite x^{2}-144 as x^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-12\right)\left(x+12\right)=0$$

To find equation solutions, solve x-12=0 and x+12=0.

$$x=12 x=-12$$

Steps by Finding Square Root

Calculate 7.2 to the power of 2 and get 51.84.

$$51.84+9.6^{2}=x^{2}$$

Calculate 9.6 to the power of 2 and get 92.16.

$$51.84+92.16=x^{2}$$

Add 51.84 and 92.16 to get 144.

$$144=x^{2}$$

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

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

Calculate 7.2 to the power of 2 and get 51.84.

$$51.84+9.6^{2}=x^{2}$$

Calculate 9.6 to the power of 2 and get 92.16.

$$51.84+92.16=x^{2}$$

Add 51.84 and 92.16 to get 144.

$$144=x^{2}$$

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

$$x^{2}=144$$

Subtract 144 from both sides.

$$x^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

Multiply -4 times -144.

$$x=\frac{0±\sqrt{576}}{2}$$

Take the square root of 576.

$$x=\frac{0±24}{2}$$

Now solve the equation x=\frac{0±24}{2} when ± is plus. Divide 24 by 2.

$$x=12$$

Now solve the equation x=\frac{0±24}{2} when ± is minus. Divide -24 by 2.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$