Solve 30X=-15X^2

$$30 X = - 15 X ^ { 2 }$$

Solve for X

$$X=-2$$

$$X=0$$

Steps Using Factoring

Add 15X^{2} to both sides.

$$30X+15X^{2}=0$$

Factor out X.

$$X\left(30+15X\right)=0$$

To find equation solutions, solve X=0 and 30+15X=0.

$$X=0 X=-2$$

Steps Using the Quadratic Formula

Add 15X^{2} to both sides.

$$30X+15X^{2}=0$$

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.

$$15X^{2}+30X=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 30 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$X=\frac{-30±\sqrt{30^{2}}}{2\times 15}$$

Take the square root of 30^{2}.

$$X=\frac{-30±30}{2\times 15}$$

Multiply 2 times 15.

$$X=\frac{-30±30}{30}$$

Now solve the equation X=\frac{-30±30}{30} when ± is plus. Add -30 to 30.

$$X=\frac{0}{30}$$

Divide 0 by 30.

$$X=0$$

Now solve the equation X=\frac{-30±30}{30} when ± is minus. Subtract 30 from -30.

$$X=-\frac{60}{30}$$

Divide -60 by 30.

$$X=-2$$

The equation is now solved.

$$X=0 X=-2$$

Steps for Completing the Square

Add 15X^{2} to both sides.

$$30X+15X^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$15X^{2}+30X=0$$

Divide both sides by 15.

$$\frac{15X^{2}+30X}{15}=\frac{0}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$X^{2}+\frac{30}{15}X=\frac{0}{15}$$

Divide 30 by 15.

$$X^{2}+2X=\frac{0}{15}$$

Divide 0 by 15.

$$X^{2}+2X=0$$

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$X^{2}+2X+1^{2}=1^{2}$$

Square 1.

$$X^{2}+2X+1=1$$

Factor X^{2}+2X+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(X+1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(X+1\right)^{2}}=\sqrt{1}$$

Simplify.

$$X+1=1 X+1=-1$$

Subtract 1 from both sides of the equation.

$$X=0 X=-2$$