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

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

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps Using Difference of Squares

Subtract 2 from both sides.

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

Subtract 2 from 1 to get -1.

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

Add x^{2} to both sides.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-1=0$$

Consider 4x^{2}-1. Rewrite 4x^{2}-1 as \left(2x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-1\right)\left(2x+1\right)=0$$

To find equation solutions, solve 2x-1=0 and 2x+1=0.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps by Finding Square Root

Add x^{2} to both sides.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}+1=2$$

Subtract 1 from both sides.

$$4x^{2}=2-1$$

Subtract 1 from 2 to get 1.

$$4x^{2}=1$$

Divide both sides by 4.

$$x^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

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

Subtract 2 from 1 to get -1.

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

Add x^{2} to both sides.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-1=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-1\right)}}{2\times 4}$$

Multiply -16 times -1.

$$x=\frac{0±\sqrt{16}}{2\times 4}$$

Take the square root of 16.

$$x=\frac{0±4}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4}{8}$$

Now solve the equation x=\frac{0±4}{8} when ± is plus. Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

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

Now solve the equation x=\frac{0±4}{8} when ± is minus. Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{2}$$

The equation is now solved.

$$x=\frac{1}{2} x=-\frac{1}{2}$$