Solve pix^2+3x+01415926=0

$$\pi { x }^{ 2 } +3x+01415926=0$$

Solve for x

$$x=-\frac{3}{\pi }\approx -0.954929659$$

$$x=0$$

Steps Using Factoring

Multiply 0 and 1415926 to get 0.

$$\pi x^{2}+3x+0=0$$

Anything plus zero gives itself.

$$\pi x^{2}+3x=0$$

Factor out x.

$$x\left(\pi x+3\right)=0$$

To find equation solutions, solve x=0 and \pi x+3=0.

$$x=0 x=-\frac{3}{\pi }$$

Steps Using the Quadratic Formula

Multiply 0 and 1415926 to get 0.

$$\pi x^{2}+3x+0=0$$

Anything plus zero gives itself.

$$\pi x^{2}+3x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}}}{2\pi }$$

Take the square root of 3^{2}.

$$x=\frac{-3±3}{2\pi }$$

Now solve the equation x=\frac{-3±3}{2\pi } when ± is plus. Add -3 to 3.

$$x=\frac{0}{2\pi }$$

Divide 0 by 2\pi .

$$x=0$$

Now solve the equation x=\frac{-3±3}{2\pi } when ± is minus. Subtract 3 from -3.

$$x=-\frac{6}{2\pi }$$

Divide -6 by 2\pi .

$$x=-\frac{3}{\pi }$$

The equation is now solved.

$$x=0 x=-\frac{3}{\pi }$$

Steps for Completing the Square

Multiply 0 and 1415926 to get 0.

$$\pi x^{2}+3x+0=0$$

Anything plus zero gives itself.

$$\pi x^{2}+3x=0$$

Divide both sides by \pi .

$$\frac{\pi x^{2}+3x}{\pi }=\frac{0}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$x^{2}+\frac{3}{\pi }x=\frac{0}{\pi }$$

Divide 0 by \pi .

$$x^{2}+\frac{3}{\pi }x=0$$

Divide \frac{3}{\pi }, the coefficient of the x term, by 2 to get \frac{3}{2\pi }. Then add the square of \frac{3}{2\pi } to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{3}{\pi }x+\left(\frac{3}{2\pi }\right)^{2}=\left(\frac{3}{2\pi }\right)^{2}$$

Square \frac{3}{2\pi }.

$$x^{2}+\frac{3}{\pi }x+\frac{9}{4\pi ^{2}}=\frac{9}{4\pi ^{2}}$$

Factor x^{2}+\frac{3}{\pi }x+\frac{9}{4\pi ^{2}}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{2\pi }\right)^{2}=\frac{9}{4\pi ^{2}}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{2\pi }\right)^{2}}=\sqrt{\frac{9}{4\pi ^{2}}}$$

Simplify.

$$x+\frac{3}{2\pi }=\frac{3}{2\pi } x+\frac{3}{2\pi }=-\frac{3}{2\pi }$$

Subtract \frac{3}{2\pi } from both sides of the equation.

$$x=0 x=-\frac{3}{\pi }$$