Solve 3x^2+18+4x-12-18x-2x^2=0

$$3 { x }^{ 2 } +18+4x-12-18x-2 { x }^{ 2 } =0$$

Solve for x

$$x=\sqrt{43}+7\approx 13.557438524$$

$$x=7-\sqrt{43}\approx 0.442561476$$

Steps Using the Quadratic Formula

Subtract 12 from 18 to get 6.

$$3x^{2}+6+4x-18x-2x^{2}=0$$

Combine 4x and -18x to get -14x.

$$3x^{2}+6-14x-2x^{2}=0$$

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

$$x^{2}+6-14x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}-14x+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -14 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 6}}{2}$$

Square -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 6}}{2}$$

Multiply -4 times 6.

$$x=\frac{-\left(-14\right)±\sqrt{196-24}}{2}$$

Add 196 to -24.

$$x=\frac{-\left(-14\right)±\sqrt{172}}{2}$$

Take the square root of 172.

$$x=\frac{-\left(-14\right)±2\sqrt{43}}{2}$$

The opposite of -14 is 14.

$$x=\frac{14±2\sqrt{43}}{2}$$

Now solve the equation x=\frac{14±2\sqrt{43}}{2} when ± is plus. Add 14 to 2\sqrt{43}.

$$x=\frac{2\sqrt{43}+14}{2}$$

Divide 14+2\sqrt{43} by 2.

$$x=\sqrt{43}+7$$

Now solve the equation x=\frac{14±2\sqrt{43}}{2} when ± is minus. Subtract 2\sqrt{43} from 14.

$$x=\frac{14-2\sqrt{43}}{2}$$

Divide 14-2\sqrt{43} by 2.

$$x=7-\sqrt{43}$$

The equation is now solved.

$$x=\sqrt{43}+7 x=7-\sqrt{43}$$

Steps for Completing the Square

Subtract 12 from 18 to get 6.

$$3x^{2}+6+4x-18x-2x^{2}=0$$

Combine 4x and -18x to get -14x.

$$3x^{2}+6-14x-2x^{2}=0$$

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

$$x^{2}+6-14x=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-14x=-6$$

Divide -14, the coefficient of the x term, by 2 to get -7. Then add the square of -7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-14x+\left(-7\right)^{2}=-6+\left(-7\right)^{2}$$

Square -7.

$$x^{2}-14x+49=-6+49$$

Add -6 to 49.

$$x^{2}-14x+49=43$$

Factor x^{2}-14x+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-7\right)^{2}=43$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{43}$$

Simplify.

$$x-7=\sqrt{43} x-7=-\sqrt{43}$$

Add 7 to both sides of the equation.

$$x=\sqrt{43}+7 x=7-\sqrt{43}$$