Solve 2(3x^2+1)-5=3

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

Solve for x

$$x=1$$

$$x=-1$$

Steps Using Difference of Squares

Use the distributive property to multiply 2 by 3x^{2}+1.

$$6x^{2}+2-5=3$$

Subtract 5 from 2 to get -3.

$$6x^{2}-3=3$$

Subtract 3 from both sides.

$$6x^{2}-3-3=0$$

Subtract 3 from -3 to get -6.

$$6x^{2}-6=0$$

Divide both sides by 6.

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

Consider x^{2}-1. Rewrite x^{2}-1 as x^{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).

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

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

$$x=1 x=-1$$

Steps by Finding Square Root

Use the distributive property to multiply 2 by 3x^{2}+1.

$$6x^{2}+2-5=3$$

Subtract 5 from 2 to get -3.

$$6x^{2}-3=3$$

Add 3 to both sides.

$$6x^{2}=3+3$$

Add 3 and 3 to get 6.

$$6x^{2}=6$$

Divide both sides by 6.

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

Divide 6 by 6 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2 by 3x^{2}+1.

$$6x^{2}+2-5=3$$

Subtract 5 from 2 to get -3.

$$6x^{2}-3=3$$

Subtract 3 from both sides.

$$6x^{2}-3-3=0$$

Subtract 3 from -3 to get -6.

$$6x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-6\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-6\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-6\right)}}{2\times 6}$$

Multiply -24 times -6.

$$x=\frac{0±\sqrt{144}}{2\times 6}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±12}{12}$$

Now solve the equation x=\frac{0±12}{12} when ± is plus. Divide 12 by 12.

$$x=1$$

Now solve the equation x=\frac{0±12}{12} when ± is minus. Divide -12 by 12.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$