Solve x^2/4+x^2=6

$$\frac { x ^ { 2 } } { 4 } + x ^ { 2 } = 6$$

Solve for x

$$x = \frac{2 \sqrt{30}}{5} \approx 2.19089023$$

$$x = -\frac{2 \sqrt{30}}{5} \approx -2.19089023$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$x^{2}+4x^{2}=24$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}=24$$

Divide both sides by 5.

$$x^{2}=\frac{24}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{30}}{5} x=-\frac{2\sqrt{30}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$x^{2}+4x^{2}=24$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}=24$$

Subtract 24 from both sides.

$$5x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-24\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-24\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-24\right)}}{2\times 5}$$

Multiply -20 times -24.

$$x=\frac{0±\sqrt{480}}{2\times 5}$$

Take the square root of 480.

$$x=\frac{0±4\sqrt{30}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±4\sqrt{30}}{10}$$

Now solve the equation x=\frac{0±4\sqrt{30}}{10} when ± is plus.

$$x=\frac{2\sqrt{30}}{5}$$

Now solve the equation x=\frac{0±4\sqrt{30}}{10} when ± is minus.

$$x=-\frac{2\sqrt{30}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{30}}{5} x=-\frac{2\sqrt{30}}{5}$$