Solve 8x^2-12=20

$$8 x ^ { 2 } - 12 = 20$$

Solve for x

$$x=2$$

$$x=-2$$

Steps Using Difference of Squares

Subtract 20 from both sides.

$$8x^{2}-12-20=0$$

Subtract 20 from -12 to get -32.

$$8x^{2}-32=0$$

Divide both sides by 8.

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

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

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

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

$$x=2 x=-2$$

Steps by Finding Square Root

Add 12 to both sides.

$$8x^{2}=20+12$$

Add 20 and 12 to get 32.

$$8x^{2}=32$$

Divide both sides by 8.

$$x^{2}=\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Subtract 20 from both sides.

$$8x^{2}-12-20=0$$

Subtract 20 from -12 to get -32.

$$8x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-32\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-32\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-32\right)}}{2\times 8}$$

Multiply -32 times -32.

$$x=\frac{0±\sqrt{1024}}{2\times 8}$$

Take the square root of 1024.

$$x=\frac{0±32}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±32}{16}$$

Now solve the equation x=\frac{0±32}{16} when ± is plus. Divide 32 by 16.

$$x=2$$

Now solve the equation x=\frac{0±32}{16} when ± is minus. Divide -32 by 16.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$