Solve 7x^2=-9x

$$7 x ^ { 2 } = - 9 x$$

Solve for x

$$x = -\frac{9}{7} = -1\frac{2}{7} \approx -1.285714286$$

$$x=0$$

Steps Using Factoring

Add 9x to both sides.

$$7x^{2}+9x=0$$

Factor out x.

$$x\left(7x+9\right)=0$$

To find equation solutions, solve x=0 and 7x+9=0.

$$x=0 x=-\frac{9}{7}$$

Steps Using the Quadratic Formula

Add 9x to both sides.

$$7x^{2}+9x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 9 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}}}{2\times 7}$$

Take the square root of 9^{2}.

$$x=\frac{-9±9}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{-9±9}{14}$$

Now solve the equation x=\frac{-9±9}{14} when ± is plus. Add -9 to 9.

$$x=\frac{0}{14}$$

Divide 0 by 14.

$$x=0$$

Now solve the equation x=\frac{-9±9}{14} when ± is minus. Subtract 9 from -9.

$$x=-\frac{18}{14}$$

Reduce the fraction \frac{-18}{14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{7}$$

The equation is now solved.

$$x=0 x=-\frac{9}{7}$$

Steps for Completing the Square

Add 9x to both sides.

$$7x^{2}+9x=0$$

Divide both sides by 7.

$$\frac{7x^{2}+9x}{7}=\frac{0}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x^{2}+\frac{9}{7}x=\frac{0}{7}$$

Divide 0 by 7.

$$x^{2}+\frac{9}{7}x=0$$

Divide \frac{9}{7}, the coefficient of the x term, by 2 to get \frac{9}{14}. Then add the square of \frac{9}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{9}{7}x+\left(\frac{9}{14}\right)^{2}=\left(\frac{9}{14}\right)^{2}$$

Square \frac{9}{14} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{9}{7}x+\frac{81}{196}=\frac{81}{196}$$

Factor x^{2}+\frac{9}{7}x+\frac{81}{196}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{9}{14}\right)^{2}=\frac{81}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{9}{14}\right)^{2}}=\sqrt{\frac{81}{196}}$$

Simplify.

$$x+\frac{9}{14}=\frac{9}{14} x+\frac{9}{14}=-\frac{9}{14}$$

Subtract \frac{9}{14} from both sides of the equation.

$$x=0 x=-\frac{9}{7}$$