Solve 2x^2+3x=-5x

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

Solve for x

$$x=-4$$

$$x=0$$

Steps Using Factoring

Add 5x to both sides.

$$2x^{2}+3x+5x=0$$

Combine 3x and 5x to get 8x.

$$2x^{2}+8x=0$$

Factor out x.

$$x\left(2x+8\right)=0$$

To find equation solutions, solve x=0 and 2x+8=0.

$$x=0 x=-4$$

Steps Using the Quadratic Formula

Add 5x to both sides.

$$2x^{2}+3x+5x=0$$

Combine 3x and 5x to get 8x.

$$2x^{2}+8x=0$$

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

$$x=\frac{-8±\sqrt{8^{2}}}{2\times 2}$$

Take the square root of 8^{2}.

$$x=\frac{-8±8}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-8±8}{4}$$

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

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

Divide 0 by 4.

$$x=0$$

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

$$x=-\frac{16}{4}$$

Divide -16 by 4.

$$x=-4$$

The equation is now solved.

$$x=0 x=-4$$

Steps for Completing the Square

Add 5x to both sides.

$$2x^{2}+3x+5x=0$$

Combine 3x and 5x to get 8x.

$$2x^{2}+8x=0$$

Divide both sides by 2.

$$\frac{2x^{2}+8x}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{8}{2}x=\frac{0}{2}$$

Divide 8 by 2.

$$x^{2}+4x=\frac{0}{2}$$

Divide 0 by 2.

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

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.

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

Square 2.

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

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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+2=2 x+2=-2$$

Subtract 2 from both sides of the equation.

$$x=0 x=-4$$