Solve (25x^2)div9+50xdiv3=0

$$(25 { x }^{ 2 } ) \div 9+50x \div 3=0$$

Solve for x

$$x=-6$$

$$x=0$$

Steps Using Factoring

Multiply both sides of the equation by 9, the least common multiple of 9,3.

$$25x^{2}+3\times 50x=0$$

Multiply 3 and 50 to get 150.

$$25x^{2}+150x=0$$

Factor out x.

$$x\left(25x+150\right)=0$$

To find equation solutions, solve x=0 and 25x+150=0.

$$x=0 x=-6$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 9, the least common multiple of 9,3.

$$25x^{2}+3\times 50x=0$$

Multiply 3 and 50 to get 150.

$$25x^{2}+150x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 150 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-150±\sqrt{150^{2}}}{2\times 25}$$

Take the square root of 150^{2}.

$$x=\frac{-150±150}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{-150±150}{50}$$

Now solve the equation x=\frac{-150±150}{50} when ± is plus. Add -150 to 150.

$$x=\frac{0}{50}$$

Divide 0 by 50.

$$x=0$$

Now solve the equation x=\frac{-150±150}{50} when ± is minus. Subtract 150 from -150.

$$x=-\frac{300}{50}$$

Divide -300 by 50.

$$x=-6$$

The equation is now solved.

$$x=0 x=-6$$

Steps for Completing the Square

Multiply both sides of the equation by 9, the least common multiple of 9,3.

$$25x^{2}+3\times 50x=0$$

Multiply 3 and 50 to get 150.

$$25x^{2}+150x=0$$

Divide both sides by 25.

$$\frac{25x^{2}+150x}{25}=\frac{0}{25}$$

Dividing by 25 undoes the multiplication by 25.

$$x^{2}+\frac{150}{25}x=\frac{0}{25}$$

Divide 150 by 25.

$$x^{2}+6x=\frac{0}{25}$$

Divide 0 by 25.

$$x^{2}+6x=0$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+6x+3^{2}=3^{2}$$

Square 3.

$$x^{2}+6x+9=9$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+3=3 x+3=-3$$

Subtract 3 from both sides of the equation.

$$x=0 x=-6$$