Solve {left(1/2right)}^2+2*1/x-1=14

$${ \left( \frac{ 1 }{ 2 } \right) }^{ 2 } +2 \times \frac{ 1 }{ x } -1=14$$

Solve for x

$$x=\frac{8}{59}\approx 0.13559322$$

Steps for Solving Linear Equation

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

$$x\times \left(\frac{1}{2}\right)^{2}+2\times 1+x\left(-1\right)=14x$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$x\times \frac{1}{4}+2\times 1+x\left(-1\right)=14x$$

Multiply 2 and 1 to get 2.

$$x\times \frac{1}{4}+2+x\left(-1\right)=14x$$

Combine x\times \frac{1}{4} and x\left(-1\right) to get -\frac{3}{4}x.

$$-\frac{3}{4}x+2=14x$$

Subtract 14x from both sides.

$$-\frac{3}{4}x+2-14x=0$$

Combine -\frac{3}{4}x and -14x to get -\frac{59}{4}x.

$$-\frac{59}{4}x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{59}{4}x=-2$$

Multiply both sides by -\frac{4}{59}, the reciprocal of -\frac{59}{4}.

$$x=-2\left(-\frac{4}{59}\right)$$

Express -2\left(-\frac{4}{59}\right) as a single fraction.

$$x=\frac{-2\left(-4\right)}{59}$$

Multiply -2 and -4 to get 8.

$$x=\frac{8}{59}$$