Solve (04+x)*xdiv(03-x)=45*10^-4

$$(04+x) \times x \div (03-x)=45 \times { 10 }^{ -4 }$$

Solve for x

$$x=-\frac{9}{2000}=-0.0045$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-\left(0\times 4+x\right)x=45\times 10^{-4}x$$

Multiply 0 and 4 to get 0.

$$-xx=45\times 10^{-4}x$$

Multiply x and x to get x^{2}.

$$-x^{2}=45\times 10^{-4}x$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$-x^{2}=45\times \frac{1}{10000}x$$

Multiply 45 and \frac{1}{10000} to get \frac{9}{2000}.

$$-x^{2}=\frac{9}{2000}x$$

Subtract \frac{9}{2000}x from both sides.

$$-x^{2}-\frac{9}{2000}x=0$$

Factor out x.

$$x\left(-x-\frac{9}{2000}\right)=0$$

To find equation solutions, solve x=0 and -x-\frac{9}{2000}=0.

$$x=0 x=-\frac{9}{2000}$$

Variable x cannot be equal to 0.

$$x=-\frac{9}{2000}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-\left(0\times 4+x\right)x=45\times 10^{-4}x$$

Multiply 0 and 4 to get 0.

$$-xx=45\times 10^{-4}x$$

Multiply x and x to get x^{2}.

$$-x^{2}=45\times 10^{-4}x$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$-x^{2}=45\times \frac{1}{10000}x$$

Multiply 45 and \frac{1}{10000} to get \frac{9}{2000}.

$$-x^{2}=\frac{9}{2000}x$$

Subtract \frac{9}{2000}x from both sides.

$$-x^{2}-\frac{9}{2000}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -\frac{9}{2000} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{9}{2000}\right)±\sqrt{\left(-\frac{9}{2000}\right)^{2}}}{2\left(-1\right)}$$

Take the square root of \left(-\frac{9}{2000}\right)^{2}.

$$x=\frac{-\left(-\frac{9}{2000}\right)±\frac{9}{2000}}{2\left(-1\right)}$$

The opposite of -\frac{9}{2000} is \frac{9}{2000}.

$$x=\frac{\frac{9}{2000}±\frac{9}{2000}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{\frac{9}{2000}±\frac{9}{2000}}{-2}$$

Now solve the equation x=\frac{\frac{9}{2000}±\frac{9}{2000}}{-2} when ± is plus. Add \frac{9}{2000} to \frac{9}{2000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{9}{1000}}{-2}$$

Divide \frac{9}{1000} by -2.

$$x=-\frac{9}{2000}$$

Now solve the equation x=\frac{\frac{9}{2000}±\frac{9}{2000}}{-2} when ± is minus. Subtract \frac{9}{2000} from \frac{9}{2000} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 0 by -2.

$$x=0$$

The equation is now solved.

$$x=-\frac{9}{2000} x=0$$

Variable x cannot be equal to 0.

$$x=-\frac{9}{2000}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-\left(0\times 4+x\right)x=45\times 10^{-4}x$$

Multiply 0 and 4 to get 0.

$$-xx=45\times 10^{-4}x$$

Multiply x and x to get x^{2}.

$$-x^{2}=45\times 10^{-4}x$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$-x^{2}=45\times \frac{1}{10000}x$$

Multiply 45 and \frac{1}{10000} to get \frac{9}{2000}.

$$-x^{2}=\frac{9}{2000}x$$

Subtract \frac{9}{2000}x from both sides.

$$-x^{2}-\frac{9}{2000}x=0$$

Divide both sides by -1.

$$\frac{-x^{2}-\frac{9}{2000}x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{\frac{9}{2000}}{-1}\right)x=\frac{0}{-1}$$

Divide -\frac{9}{2000} by -1.

$$x^{2}+\frac{9}{2000}x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}+\frac{9}{2000}x=0$$

Divide \frac{9}{2000}, the coefficient of the x term, by 2 to get \frac{9}{4000}. Then add the square of \frac{9}{4000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{9}{2000}x+\left(\frac{9}{4000}\right)^{2}=\left(\frac{9}{4000}\right)^{2}$$

Square \frac{9}{4000} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{9}{2000}x+\frac{81}{16000000}=\frac{81}{16000000}$$

Factor x^{2}+\frac{9}{2000}x+\frac{81}{16000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{9}{4000}\right)^{2}=\frac{81}{16000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{9}{4000}\right)^{2}}=\sqrt{\frac{81}{16000000}}$$

Simplify.

$$x+\frac{9}{4000}=\frac{9}{4000} x+\frac{9}{4000}=-\frac{9}{4000}$$

Subtract \frac{9}{4000} from both sides of the equation.

$$x=0 x=-\frac{9}{2000}$$

Variable x cannot be equal to 0.

$$x=-\frac{9}{2000}$$