Solve x-5.6+6.4/x=0

$$x-5.6+ \frac{ 6.4 }{ x } =0$$

Solve for x

$$x=4$$

$$x=1.6$$

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.

$$xx+x\left(-5.6\right)+6.4=0$$

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

$$x^{2}+x\left(-5.6\right)+6.4=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}-5.6x+6.4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -5.6 for b, and 6.4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5.6\right)±\sqrt{\left(-5.6\right)^{2}-4\times 6.4}}{2}$$

Square -5.6 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-5.6\right)±\sqrt{31.36-4\times 6.4}}{2}$$

Multiply -4 times 6.4.

$$x=\frac{-\left(-5.6\right)±\sqrt{31.36-25.6}}{2}$$

Add 31.36 to -25.6 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-5.6\right)±\sqrt{5.76}}{2}$$

Take the square root of 5.76.

$$x=\frac{-\left(-5.6\right)±\frac{12}{5}}{2}$$

The opposite of -5.6 is 5.6.

$$x=\frac{5.6±\frac{12}{5}}{2}$$

Now solve the equation x=\frac{5.6±\frac{12}{5}}{2} when ± is plus. Add 5.6 to \frac{12}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{8}{2}$$

Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{5.6±\frac{12}{5}}{2} when ± is minus. Subtract \frac{12}{5} from 5.6 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{16}{5}}{2}$$

Divide \frac{16}{5} by 2.

$$x=\frac{8}{5}$$

The equation is now solved.

$$x=4 x=\frac{8}{5}$$

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.

$$xx+x\left(-5.6\right)+6.4=0$$

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

$$x^{2}+x\left(-5.6\right)+6.4=0$$

Subtract 6.4 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+x\left(-5.6\right)=-6.4$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}-5.6x=-6.4$$

Divide -5.6, the coefficient of the x term, by 2 to get -2.8. Then add the square of -2.8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-5.6x+\left(-2.8\right)^{2}=-6.4+\left(-2.8\right)^{2}$$

Square -2.8 by squaring both the numerator and the denominator of the fraction.

$$x^{2}-5.6x+7.84=-6.4+7.84$$

Add -6.4 to 7.84 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-5.6x+7.84=1.44$$

Factor x^{2}-5.6x+7.84. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2.8\right)^{2}=1.44$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2.8\right)^{2}}=\sqrt{1.44}$$

Simplify.

$$x-2.8=\frac{6}{5} x-2.8=-\frac{6}{5}$$

Add 2.8 to both sides of the equation.

$$x=4 x=\frac{8}{5}$$