Solve x^2+25/9x^2=50

$$x ^ { 2 } + \frac { 25 } { 9 } x ^ { 2 } = 50$$

Solve for x

$$x = \frac{15 \sqrt{17}}{17} \approx 3.638034376$$

$$x = -\frac{15 \sqrt{17}}{17} \approx -3.638034376$$

Steps by Finding Square Root

Combine x^{2} and \frac{25}{9}x^{2} to get \frac{34}{9}x^{2}.

$$\frac{34}{9}x^{2}=50$$

Multiply both sides by \frac{9}{34}, the reciprocal of \frac{34}{9}.

$$x^{2}=50\times \frac{9}{34}$$

Multiply 50 and \frac{9}{34} to get \frac{225}{17}.

$$x^{2}=\frac{225}{17}$$

Take the square root of both sides of the equation.

$$x=\frac{15\sqrt{17}}{17} x=-\frac{15\sqrt{17}}{17}$$

Steps Using the Quadratic Formula

Combine x^{2} and \frac{25}{9}x^{2} to get \frac{34}{9}x^{2}.

$$\frac{34}{9}x^{2}=50$$

Subtract 50 from both sides.

$$\frac{34}{9}x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{34}{9} for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{34}{9}\left(-50\right)}}{2\times \frac{34}{9}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{34}{9}\left(-50\right)}}{2\times \frac{34}{9}}$$

Multiply -4 times \frac{34}{9}.

$$x=\frac{0±\sqrt{-\frac{136}{9}\left(-50\right)}}{2\times \frac{34}{9}}$$

Multiply -\frac{136}{9} times -50.

$$x=\frac{0±\sqrt{\frac{6800}{9}}}{2\times \frac{34}{9}}$$

Take the square root of \frac{6800}{9}.

$$x=\frac{0±\frac{20\sqrt{17}}{3}}{2\times \frac{34}{9}}$$

Multiply 2 times \frac{34}{9}.

$$x=\frac{0±\frac{20\sqrt{17}}{3}}{\frac{68}{9}}$$

Now solve the equation x=\frac{0±\frac{20\sqrt{17}}{3}}{\frac{68}{9}} when ± is plus.

$$x=\frac{15\sqrt{17}}{17}$$

Now solve the equation x=\frac{0±\frac{20\sqrt{17}}{3}}{\frac{68}{9}} when ± is minus.

$$x=-\frac{15\sqrt{17}}{17}$$

The equation is now solved.

$$x=\frac{15\sqrt{17}}{17} x=-\frac{15\sqrt{17}}{17}$$