Solve 2x^2+3x^2-1=0

$$2 { x }^{ 2 } +3 { x }^{ 2 } -1=0$$

Solve for x

$$x=\frac{\sqrt{5}}{5}\approx 0.447213595$$

$$x=-\frac{\sqrt{5}}{5}\approx -0.447213595$$

Steps by Finding Square Root

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$5x^{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$5x^{2}=1$$

Divide both sides by 5.

$$x^{2}=\frac{1}{5}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$5x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-1\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-1\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-1\right)}}{2\times 5}$$

Multiply -20 times -1.

$$x=\frac{0±\sqrt{20}}{2\times 5}$$

Take the square root of 20.

$$x=\frac{0±2\sqrt{5}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{5}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{5}}{10} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{5}}{10} when ± is minus.

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

The equation is now solved.

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