Solve 2x+2/21,1=8,43/x

$$\frac { 2 x + 2 } { 21,1 } = \frac { 8,43 } { x }$$

Solve for x

$$x=\frac{\sqrt{891865}}{100}-0,5\approx 8.943860439$$

$$x=-\frac{\sqrt{891865}}{100}-0,5\approx -9.943860439$$

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.

$$x\times \frac{2x+2}{21,1}=8,43$$

Divide each term of 2x+2 by 21,1 to get \frac{2x}{21,1}+\frac{2}{21,1}.

$$x\left(\frac{2x}{21,1}+\frac{2}{21,1}\right)=8,43$$

Divide 2x by 21,1 to get \frac{20}{211}x.

$$x\left(\frac{20}{211}x+\frac{2}{21,1}\right)=8,43$$

Expand \frac{2}{21,1} by multiplying both numerator and the denominator by 10.

$$x\left(\frac{20}{211}x+\frac{20}{211}\right)=8,43$$

Use the distributive property to multiply x by \frac{20}{211}x+\frac{20}{211}.

$$\frac{20}{211}x^{2}+x\times \frac{20}{211}=8,43$$

Subtract 8,43 from both sides.

$$\frac{20}{211}x^{2}+x\times \frac{20}{211}-8,43=0$$

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.

$$\frac{20}{211}x^{2}+\frac{20}{211}x-8,43=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{20}{211} for a, \frac{20}{211} for b, and -8,43 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{20}{211}±\sqrt{\frac{20}{211}^{2}-4\times \frac{20}{211}\left(-8,43\right)}}{2\times \frac{20}{211}}$$

Square \frac{20}{211} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{20}{211}±\sqrt{\frac{400}{44521}-4\times \frac{20}{211}\left(-8,43\right)}}{2\times \frac{20}{211}}$$

Multiply -4 times \frac{20}{211}.

$$x=\frac{-\frac{20}{211}±\sqrt{\frac{400}{44521}-\frac{80}{211}\left(-8,43\right)}}{2\times \frac{20}{211}}$$

Multiply -\frac{80}{211} times -8,43 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{20}{211}±\sqrt{\frac{400}{44521}+\frac{3372}{1055}}}{2\times \frac{20}{211}}$$

Add \frac{400}{44521} to \frac{3372}{1055} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{20}{211}±\sqrt{\frac{713492}{222605}}}{2\times \frac{20}{211}}$$

Take the square root of \frac{713492}{222605}.

$$x=\frac{-\frac{20}{211}±\frac{2\sqrt{891865}}{1055}}{2\times \frac{20}{211}}$$

Multiply 2 times \frac{20}{211}.

$$x=\frac{-\frac{20}{211}±\frac{2\sqrt{891865}}{1055}}{\frac{40}{211}}$$

Now solve the equation x=\frac{-\frac{20}{211}±\frac{2\sqrt{891865}}{1055}}{\frac{40}{211}} when ± is plus. Add -\frac{20}{211} to \frac{2\sqrt{891865}}{1055}.

$$x=\frac{\frac{2\sqrt{891865}}{1055}-\frac{20}{211}}{\frac{40}{211}}$$

Divide -\frac{20}{211}+\frac{2\sqrt{891865}}{1055} by \frac{40}{211} by multiplying -\frac{20}{211}+\frac{2\sqrt{891865}}{1055} by the reciprocal of \frac{40}{211}.

$$x=\frac{\sqrt{891865}}{100}-\frac{1}{2}$$

Now solve the equation x=\frac{-\frac{20}{211}±\frac{2\sqrt{891865}}{1055}}{\frac{40}{211}} when ± is minus. Subtract \frac{2\sqrt{891865}}{1055} from -\frac{20}{211}.

$$x=\frac{-\frac{2\sqrt{891865}}{1055}-\frac{20}{211}}{\frac{40}{211}}$$

Divide -\frac{20}{211}-\frac{2\sqrt{891865}}{1055} by \frac{40}{211} by multiplying -\frac{20}{211}-\frac{2\sqrt{891865}}{1055} by the reciprocal of \frac{40}{211}.

$$x=-\frac{\sqrt{891865}}{100}-\frac{1}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{891865}}{100}-\frac{1}{2} x=-\frac{\sqrt{891865}}{100}-\frac{1}{2}$$

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.

$$x\times \frac{2x+2}{21,1}=8,43$$

Divide each term of 2x+2 by 21,1 to get \frac{2x}{21,1}+\frac{2}{21,1}.

$$x\left(\frac{2x}{21,1}+\frac{2}{21,1}\right)=8,43$$

Divide 2x by 21,1 to get \frac{20}{211}x.

$$x\left(\frac{20}{211}x+\frac{2}{21,1}\right)=8,43$$

Expand \frac{2}{21,1} by multiplying both numerator and the denominator by 10.

$$x\left(\frac{20}{211}x+\frac{20}{211}\right)=8,43$$

Use the distributive property to multiply x by \frac{20}{211}x+\frac{20}{211}.

$$\frac{20}{211}x^{2}+x\times \frac{20}{211}=8,43$$

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.

$$\frac{20}{211}x^{2}+\frac{20}{211}x=8,43$$

Divide both sides of the equation by \frac{20}{211}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{20}{211}x^{2}+\frac{20}{211}x}{\frac{20}{211}}=\frac{8,43}{\frac{20}{211}}$$

Dividing by \frac{20}{211} undoes the multiplication by \frac{20}{211}.

$$x^{2}+\frac{\frac{20}{211}}{\frac{20}{211}}x=\frac{8,43}{\frac{20}{211}}$$

Divide \frac{20}{211} by \frac{20}{211} by multiplying \frac{20}{211} by the reciprocal of \frac{20}{211}.

$$x^{2}+x=\frac{8,43}{\frac{20}{211}}$$

Divide 8,43 by \frac{20}{211} by multiplying 8,43 by the reciprocal of \frac{20}{211}.

$$x^{2}+x=88,9365$$

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=88,9365+\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+x+\frac{1}{4}=88,9365+\frac{1}{4}$$

Add 88,9365 to \frac{1}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+x+\frac{1}{4}=\frac{178373}{2000}$$

Factor x^{2}+x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{178373}{2000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{178373}{2000}}$$

Simplify.

$$x+\frac{1}{2}=\frac{\sqrt{891865}}{100} x+\frac{1}{2}=-\frac{\sqrt{891865}}{100}$$

Subtract \frac{1}{2} from both sides of the equation.

$$x=\frac{\sqrt{891865}}{100}-\frac{1}{2} x=-\frac{\sqrt{891865}}{100}-\frac{1}{2}$$