Solve -2x^2+34x+2x=0

$$- 2 x ^ { 2 } + 34 x + 2 x = 0$$

Solve for x

$$x=18$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(-2x+34+2\right)=0$$

To find equation solutions, solve x=0 and -2x+36=0.

$$x=0 x=18$$

Steps Using the Quadratic Formula

Combine 34x and 2x to get 36x.

$$-2x^{2}+36x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 36 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-36±\sqrt{36^{2}}}{2\left(-2\right)}$$

Take the square root of 36^{2}.

$$x=\frac{-36±36}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-36±36}{-4}$$

Now solve the equation x=\frac{-36±36}{-4} when ± is plus. Add -36 to 36.

$$x=\frac{0}{-4}$$

Divide 0 by -4.

$$x=0$$

Now solve the equation x=\frac{-36±36}{-4} when ± is minus. Subtract 36 from -36.

$$x=-\frac{72}{-4}$$

Divide -72 by -4.

$$x=18$$

The equation is now solved.

$$x=0 x=18$$

Steps for Completing the Square

Combine 34x and 2x to get 36x.

$$-2x^{2}+36x=0$$

Divide both sides by -2.

$$\frac{-2x^{2}+36x}{-2}=\frac{0}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\frac{36}{-2}x=\frac{0}{-2}$$

Divide 36 by -2.

$$x^{2}-18x=\frac{0}{-2}$$

Divide 0 by -2.

$$x^{2}-18x=0$$

Divide -18, the coefficient of the x term, by 2 to get -9. Then add the square of -9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-18x+\left(-9\right)^{2}=\left(-9\right)^{2}$$

Square -9.

$$x^{2}-18x+81=81$$

Factor x^{2}-18x+81. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-9\right)^{2}=81$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{81}$$

Simplify.

$$x-9=9 x-9=-9$$

Add 9 to both sides of the equation.

$$x=18 x=0$$