Solve 853/1280=x/xx

$$\frac{ 853 }{ 1280 } = \frac{ x }{ xx }$$

Solve for x

$$x = \frac{1280}{853} = 1\frac{427}{853} \approx 1.500586166$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1280x^{2}, the least common multiple of 1280,xx.

$$853x^{2}=1280x$$

Subtract 1280x from both sides.

$$853x^{2}-1280x=0$$

Factor out x.

$$x\left(853x-1280\right)=0$$

To find equation solutions, solve x=0 and 853x-1280=0.

$$x=0 x=\frac{1280}{853}$$

Variable x cannot be equal to 0.

$$x=\frac{1280}{853}$$

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 1280x^{2}, the least common multiple of 1280,xx.

$$853x^{2}=1280x$$

Subtract 1280x from both sides.

$$853x^{2}-1280x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 853 for a, -1280 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1280\right)±\sqrt{\left(-1280\right)^{2}}}{2\times 853}$$

Take the square root of \left(-1280\right)^{2}.

$$x=\frac{-\left(-1280\right)±1280}{2\times 853}$$

The opposite of -1280 is 1280.

$$x=\frac{1280±1280}{2\times 853}$$

Multiply 2 times 853.

$$x=\frac{1280±1280}{1706}$$

Now solve the equation x=\frac{1280±1280}{1706} when ± is plus. Add 1280 to 1280.

$$x=\frac{2560}{1706}$$

Reduce the fraction \frac{2560}{1706} to lowest terms by extracting and canceling out 2.

$$x=\frac{1280}{853}$$

Now solve the equation x=\frac{1280±1280}{1706} when ± is minus. Subtract 1280 from 1280.

$$x=\frac{0}{1706}$$

Divide 0 by 1706.

$$x=0$$

The equation is now solved.

$$x=\frac{1280}{853} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{1280}{853}$$

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 1280x^{2}, the least common multiple of 1280,xx.

$$853x^{2}=1280x$$

Subtract 1280x from both sides.

$$853x^{2}-1280x=0$$

Divide both sides by 853.

$$\frac{853x^{2}-1280x}{853}=\frac{0}{853}$$

Dividing by 853 undoes the multiplication by 853.

$$x^{2}-\frac{1280}{853}x=\frac{0}{853}$$

Divide 0 by 853.

$$x^{2}-\frac{1280}{853}x=0$$

Divide -\frac{1280}{853}, the coefficient of the x term, by 2 to get -\frac{640}{853}. Then add the square of -\frac{640}{853} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1280}{853}x+\left(-\frac{640}{853}\right)^{2}=\left(-\frac{640}{853}\right)^{2}$$

Square -\frac{640}{853} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1280}{853}x+\frac{409600}{727609}=\frac{409600}{727609}$$

Factor x^{2}-\frac{1280}{853}x+\frac{409600}{727609}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{640}{853}\right)^{2}=\frac{409600}{727609}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{640}{853}\right)^{2}}=\sqrt{\frac{409600}{727609}}$$

Simplify.

$$x-\frac{640}{853}=\frac{640}{853} x-\frac{640}{853}=-\frac{640}{853}$$

Add \frac{640}{853} to both sides of the equation.

$$x=\frac{1280}{853} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{1280}{853}$$