Solve 3x^2+1=x^2+5

$$3 x ^ { 2 } + 1 = x ^ { 2 } + 5$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Subtract x^{2} from both sides.

$$3x^{2}+1-x^{2}=5$$

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

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

Subtract 1 from both sides.

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

Subtract 1 from 5 to get 4.

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

Divide both sides by 2.

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

Divide 4 by 2 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

$$x=\sqrt{2} x=-\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract x^{2} from both sides.

$$3x^{2}+1-x^{2}=5$$

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

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

Subtract 5 from both sides.

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

Subtract 5 from 1 to get -4.

$$2x^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-4\right)}}{2\times 2}$$

Multiply -8 times -4.

$$x=\frac{0±\sqrt{32}}{2\times 2}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{4} when ± is plus.

$$x=\sqrt{2}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{4} when ± is minus.

$$x=-\sqrt{2}$$

The equation is now solved.

$$x=\sqrt{2} x=-\sqrt{2}$$