Solve 2x^2+x^2-5=0

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

Solve for x

$$x = \frac{\sqrt{15}}{3} \approx 1.290994449$$

$$x = -\frac{\sqrt{15}}{3} \approx -1.290994449$$

Steps by Finding Square Root

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-5=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$3x^{2}=5$$

Divide both sides by 3.

$$x^{2}=\frac{5}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{3} x=-\frac{\sqrt{15}}{3}$$

Steps Using the Quadratic Formula

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-5\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-5\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-5\right)}}{2\times 3}$$

Multiply -12 times -5.

$$x=\frac{0±\sqrt{60}}{2\times 3}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{15}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{6} when ± is plus.

$$x=\frac{\sqrt{15}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{6} when ± is minus.

$$x=-\frac{\sqrt{15}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{3} x=-\frac{\sqrt{15}}{3}$$