Solve 10x^2=-17x

$$10 x ^ { 2 } = - 17 x$$

Solve for x

$$x = -\frac{17}{10} = -1\frac{7}{10} = -1.7$$

$$x=0$$

Steps Using Factoring

Add 17x to both sides.

$$10x^{2}+17x=0$$

Factor out x.

$$x\left(10x+17\right)=0$$

To find equation solutions, solve x=0 and 10x+17=0.

$$x=0 x=-\frac{17}{10}$$

Steps Using the Quadratic Formula

Add 17x to both sides.

$$10x^{2}+17x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 17 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}}}{2\times 10}$$

Take the square root of 17^{2}.

$$x=\frac{-17±17}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{-17±17}{20}$$

Now solve the equation x=\frac{-17±17}{20} when ± is plus. Add -17 to 17.

$$x=\frac{0}{20}$$

Divide 0 by 20.

$$x=0$$

Now solve the equation x=\frac{-17±17}{20} when ± is minus. Subtract 17 from -17.

$$x=-\frac{34}{20}$$

Reduce the fraction \frac{-34}{20} to lowest terms by extracting and canceling out 2.

$$x=-\frac{17}{10}$$

The equation is now solved.

$$x=0 x=-\frac{17}{10}$$

Steps for Completing the Square

Add 17x to both sides.

$$10x^{2}+17x=0$$

Divide both sides by 10.

$$\frac{10x^{2}+17x}{10}=\frac{0}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x^{2}+\frac{17}{10}x=\frac{0}{10}$$

Divide 0 by 10.

$$x^{2}+\frac{17}{10}x=0$$

Divide \frac{17}{10}, the coefficient of the x term, by 2 to get \frac{17}{20}. Then add the square of \frac{17}{20} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{17}{10}x+\left(\frac{17}{20}\right)^{2}=\left(\frac{17}{20}\right)^{2}$$

Square \frac{17}{20} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{17}{10}x+\frac{289}{400}=\frac{289}{400}$$

Factor x^{2}+\frac{17}{10}x+\frac{289}{400}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{17}{20}\right)^{2}=\frac{289}{400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{17}{20}\right)^{2}}=\sqrt{\frac{289}{400}}$$

Simplify.

$$x+\frac{17}{20}=\frac{17}{20} x+\frac{17}{20}=-\frac{17}{20}$$

Subtract \frac{17}{20} from both sides of the equation.

$$x=0 x=-\frac{17}{10}$$