Solve x^2+16/9x^2=4

$$x ^ { 2 } + \frac { 16 } { 9 } x ^ { 2 } = 4$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps Using Difference of Squares

Combine x^{2} and \frac{16}{9}x^{2} to get \frac{25}{9}x^{2}.

$$\frac{25}{9}x^{2}=4$$

Subtract 4 from both sides.

$$\frac{25}{9}x^{2}-4=0$$

Multiply both sides by 9.

$$25x^{2}-36=0$$

Consider 25x^{2}-36. Rewrite 25x^{2}-36 as \left(5x\right)^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-6\right)\left(5x+6\right)=0$$

To find equation solutions, solve 5x-6=0 and 5x+6=0.

$$x=\frac{6}{5} x=-\frac{6}{5}$$

Steps by Finding Square Root

Combine x^{2} and \frac{16}{9}x^{2} to get \frac{25}{9}x^{2}.

$$\frac{25}{9}x^{2}=4$$

Multiply both sides by \frac{9}{25}, the reciprocal of \frac{25}{9}.

$$x^{2}=4\times \frac{9}{25}$$

Multiply 4 and \frac{9}{25} to get \frac{36}{25}.

$$x^{2}=\frac{36}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{6}{5} x=-\frac{6}{5}$$

Steps Using the Quadratic Formula

Combine x^{2} and \frac{16}{9}x^{2} to get \frac{25}{9}x^{2}.

$$\frac{25}{9}x^{2}=4$$

Subtract 4 from both sides.

$$\frac{25}{9}x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{25}{9} for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{25}{9}\left(-4\right)}}{2\times \frac{25}{9}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{25}{9}\left(-4\right)}}{2\times \frac{25}{9}}$$

Multiply -4 times \frac{25}{9}.

$$x=\frac{0±\sqrt{-\frac{100}{9}\left(-4\right)}}{2\times \frac{25}{9}}$$

Multiply -\frac{100}{9} times -4.

$$x=\frac{0±\sqrt{\frac{400}{9}}}{2\times \frac{25}{9}}$$

Take the square root of \frac{400}{9}.

$$x=\frac{0±\frac{20}{3}}{2\times \frac{25}{9}}$$

Multiply 2 times \frac{25}{9}.

$$x=\frac{0±\frac{20}{3}}{\frac{50}{9}}$$

Now solve the equation x=\frac{0±\frac{20}{3}}{\frac{50}{9}} when ± is plus.

$$x=\frac{6}{5}$$

Now solve the equation x=\frac{0±\frac{20}{3}}{\frac{50}{9}} when ± is minus.

$$x=-\frac{6}{5}$$

The equation is now solved.

$$x=\frac{6}{5} x=-\frac{6}{5}$$