Solve x^2+{left(3/5right)}^2=1

$${ x }^{ 2 } + { \left( \frac{ 3 }{ 5 } \right) }^{ 2 } =1$$

Solve for x

$$x=\frac{4}{5}=0.8$$

$$x=-\frac{4}{5}=-0.8$$

Steps Using Difference of Squares

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$x^{2}+\frac{9}{25}=1$$

Subtract 1 from both sides.

$$x^{2}+\frac{9}{25}-1=0$$

Subtract 1 from \frac{9}{25} to get -\frac{16}{25}.

$$x^{2}-\frac{16}{25}=0$$

Multiply both sides by 25.

$$25x^{2}-16=0$$

Consider 25x^{2}-16. Rewrite 25x^{2}-16 as \left(5x\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-4\right)\left(5x+4\right)=0$$

To find equation solutions, solve 5x-4=0 and 5x+4=0.

$$x=\frac{4}{5} x=-\frac{4}{5}$$

Steps by Finding Square Root

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$x^{2}+\frac{9}{25}=1$$

Subtract \frac{9}{25} from both sides.

$$x^{2}=1-\frac{9}{25}$$

Subtract \frac{9}{25} from 1 to get \frac{16}{25}.

$$x^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{4}{5} x=-\frac{4}{5}$$

Steps Using the Quadratic Formula

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$x^{2}+\frac{9}{25}=1$$

Subtract 1 from both sides.

$$x^{2}+\frac{9}{25}-1=0$$

Subtract 1 from \frac{9}{25} to get -\frac{16}{25}.

$$x^{2}-\frac{16}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{25}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{16}{25}\right)}}{2}$$

Multiply -4 times -\frac{16}{25}.

$$x=\frac{0±\sqrt{\frac{64}{25}}}{2}$$

Take the square root of \frac{64}{25}.

$$x=\frac{0±\frac{8}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{8}{5}}{2} when ± is plus.

$$x=\frac{4}{5}$$

Now solve the equation x=\frac{0±\frac{8}{5}}{2} when ± is minus.

$$x=-\frac{4}{5}$$

The equation is now solved.

$$x=\frac{4}{5} x=-\frac{4}{5}$$