Solve 2x^2-8x-2*12=0

$$2 { x }^{ 2 } -8x-2 \times 12 = 0$$

Solve for x

$$x=-2$$

$$x=6$$

Steps Using Factoring By Grouping

Multiply 2 and 12 to get 24.

$$2x^{2}-8x-24=0$$

Divide both sides by 2.

$$x^{2}-4x-12=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-12. To find a and b, set up a system to be solved.

$$a+b=-4 ab=1\left(-12\right)=-12$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -12.

$$1,-12 2,-6 3,-4$$

Calculate the sum for each pair.

$$1-12=-11 2-6=-4 3-4=-1$$

The solution is the pair that gives sum -4.

$$a=-6 b=2$$

Rewrite x^{2}-4x-12 as \left(x^{2}-6x\right)+\left(2x-12\right).

$$\left(x^{2}-6x\right)+\left(2x-12\right)$$

Factor out x in the first and 2 in the second group.

$$x\left(x-6\right)+2\left(x-6\right)$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x+2\right)$$

To find equation solutions, solve x-6=0 and x+2=0.

$$x=6 x=-2$$

Steps Using the Quadratic Formula

Multiply 2 and 12 to get 24.

$$2x^{2}-8x-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -8 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-24\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-24\right)}}{2\times 2}$$

Multiply -8 times -24.

$$x=\frac{-\left(-8\right)±\sqrt{64+192}}{2\times 2}$$

Add 64 to 192.

$$x=\frac{-\left(-8\right)±\sqrt{256}}{2\times 2}$$

Take the square root of 256.

$$x=\frac{-\left(-8\right)±16}{2\times 2}$$

The opposite of -8 is 8.

$$x=\frac{8±16}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{8±16}{4}$$

Now solve the equation x=\frac{8±16}{4} when ± is plus. Add 8 to 16.

$$x=\frac{24}{4}$$

Divide 24 by 4.

$$x=6$$

Now solve the equation x=\frac{8±16}{4} when ± is minus. Subtract 16 from 8.

$$x=-\frac{8}{4}$$

Divide -8 by 4.

$$x=-2$$

The equation is now solved.

$$x=6 x=-2$$

Steps for Completing the Square

Multiply 2 and 12 to get 24.

$$2x^{2}-8x-24=0$$

Add 24 to both sides. Anything plus zero gives itself.

$$2x^{2}-8x=24$$

Divide both sides by 2.

$$\frac{2x^{2}-8x}{2}=\frac{24}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{8}{2}\right)x=\frac{24}{2}$$

Divide -8 by 2.

$$x^{2}-4x=\frac{24}{2}$$

Divide 24 by 2.

$$x^{2}-4x=12$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=12+\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=12+4$$

Add 12 to 4.

$$x^{2}-4x+4=16$$

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{16}$$

Simplify.

$$x-2=4 x-2=-4$$

Add 2 to both sides of the equation.

$$x=6 x=-2$$