Solve 24*10^8=039+x/(027-x)(043-x)

$$24 \times { 10 }^{ 8 } = \frac{ 039+x }{ (027-x)(043-x) }$$

Solve for x

$$x=\frac{1}{2400000000}\approx 4.166666667 \cdot 10^{-10}$$

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^{2}.

$$24\times 10^{8}x^{2}=0\times 39+x$$

Calculate 10 to the power of 8 and get 100000000.

$$24\times 100000000x^{2}=0\times 39+x$$

Multiply 24 and 100000000 to get 2400000000.

$$2400000000x^{2}=0\times 39+x$$

Multiply 0 and 39 to get 0.

$$2400000000x^{2}=0+x$$

Anything plus zero gives itself.

$$2400000000x^{2}=x$$

Subtract x from both sides.

$$2400000000x^{2}-x=0$$

Factor out x.

$$x\left(2400000000x-1\right)=0$$

To find equation solutions, solve x=0 and 2400000000x-1=0.

$$x=0 x=\frac{1}{2400000000}$$

Variable x cannot be equal to 0.

$$x=\frac{1}{2400000000}$$

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^{2}.

$$24\times 10^{8}x^{2}=0\times 39+x$$

Calculate 10 to the power of 8 and get 100000000.

$$24\times 100000000x^{2}=0\times 39+x$$

Multiply 24 and 100000000 to get 2400000000.

$$2400000000x^{2}=0\times 39+x$$

Multiply 0 and 39 to get 0.

$$2400000000x^{2}=0+x$$

Anything plus zero gives itself.

$$2400000000x^{2}=x$$

Subtract x from both sides.

$$2400000000x^{2}-x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2400000000 for a, -1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 2400000000}$$

Take the square root of 1.

$$x=\frac{-\left(-1\right)±1}{2\times 2400000000}$$

The opposite of -1 is 1.

$$x=\frac{1±1}{2\times 2400000000}$$

Multiply 2 times 2400000000.

$$x=\frac{1±1}{4800000000}$$

Now solve the equation x=\frac{1±1}{4800000000} when ± is plus. Add 1 to 1.

$$x=\frac{2}{4800000000}$$

Reduce the fraction \frac{2}{4800000000} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{2400000000}$$

Now solve the equation x=\frac{1±1}{4800000000} when ± is minus. Subtract 1 from 1.

$$x=\frac{0}{4800000000}$$

Divide 0 by 4800000000.

$$x=0$$

The equation is now solved.

$$x=\frac{1}{2400000000} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{1}{2400000000}$$

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^{2}.

$$24\times 10^{8}x^{2}=0\times 39+x$$

Calculate 10 to the power of 8 and get 100000000.

$$24\times 100000000x^{2}=0\times 39+x$$

Multiply 24 and 100000000 to get 2400000000.

$$2400000000x^{2}=0\times 39+x$$

Multiply 0 and 39 to get 0.

$$2400000000x^{2}=0+x$$

Anything plus zero gives itself.

$$2400000000x^{2}=x$$

Subtract x from both sides.

$$2400000000x^{2}-x=0$$

Divide both sides by 2400000000.

$$\frac{2400000000x^{2}-x}{2400000000}=\frac{0}{2400000000}$$

Dividing by 2400000000 undoes the multiplication by 2400000000.

$$x^{2}-\frac{1}{2400000000}x=\frac{0}{2400000000}$$

Divide 0 by 2400000000.

$$x^{2}-\frac{1}{2400000000}x=0$$

Divide -\frac{1}{2400000000}, the coefficient of the x term, by 2 to get -\frac{1}{4800000000}. Then add the square of -\frac{1}{4800000000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{2400000000}x+\left(-\frac{1}{4800000000}\right)^{2}=\left(-\frac{1}{4800000000}\right)^{2}$$

Square -\frac{1}{4800000000} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1}{2400000000}x+\frac{1}{23040000000000000000}=\frac{1}{23040000000000000000}$$

Factor x^{2}-\frac{1}{2400000000}x+\frac{1}{23040000000000000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{4800000000}\right)^{2}=\frac{1}{23040000000000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{4800000000}\right)^{2}}=\sqrt{\frac{1}{23040000000000000000}}$$

Simplify.

$$x-\frac{1}{4800000000}=\frac{1}{4800000000} x-\frac{1}{4800000000}=-\frac{1}{4800000000}$$

Add \frac{1}{4800000000} to both sides of the equation.

$$x=\frac{1}{2400000000} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{1}{2400000000}$$