Solve x^2+2.4^2=3^2

$$x ^ { 2 } + 2.4 ^ { 2 } = 3 ^ { 2 }$$

Solve for x

$$x=1.8$$

$$x=-1.8$$

Steps Using Difference of Squares

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}+5.76=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+5.76=9$$

Subtract 9 from both sides.

$$x^{2}+5.76-9=0$$

Subtract 9 from 5.76 to get -3.24.

$$x^{2}-3.24=0$$

Consider x^{2}-3.24. Rewrite x^{2}-3.24 as x^{2}-\left(\frac{9}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{9}{5}\right)\left(x+\frac{9}{5}\right)=0$$

To find equation solutions, solve x-\frac{9}{5}=0 and x+\frac{9}{5}=0.

$$x=\frac{9}{5} x=-\frac{9}{5}$$

Steps by Finding Square Root

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}+5.76=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+5.76=9$$

Subtract 5.76 from both sides.

$$x^{2}=9-5.76$$

Subtract 5.76 from 9 to get 3.24.

$$x^{2}=3.24$$

Take the square root of both sides of the equation.

$$x=\frac{9}{5} x=-\frac{9}{5}$$

Steps Using the Quadratic Formula

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}+5.76=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+5.76=9$$

Subtract 9 from both sides.

$$x^{2}+5.76-9=0$$

Subtract 9 from 5.76 to get -3.24.

$$x^{2}-3.24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3.24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3.24\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3.24\right)}}{2}$$

Multiply -4 times -3.24.

$$x=\frac{0±\sqrt{12.96}}{2}$$

Take the square root of 12.96.

$$x=\frac{0±\frac{18}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{18}{5}}{2} when ± is plus.

$$x=\frac{9}{5}$$

Now solve the equation x=\frac{0±\frac{18}{5}}{2} when ± is minus.

$$x=-\frac{9}{5}$$

The equation is now solved.

$$x=\frac{9}{5} x=-\frac{9}{5}$$