Solve {left(53/16right)}^2+1=1/x^

$${ \left( \frac{ 53 }{ 16 } \right) }^{ 2 } +1= \frac{ 1 }{ { x }^{ } }$$

Solve for x

$$x=\frac{256}{3065}\approx 0.083523654$$

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.

$$x\times \left(\frac{53}{16}\right)^{2}+x=1$$

Calculate \frac{53}{16} to the power of 2 and get \frac{2809}{256}.

$$x\times \frac{2809}{256}+x=1$$

Combine x\times \frac{2809}{256} and x to get \frac{3065}{256}x.

$$\frac{3065}{256}x=1$$

Multiply both sides by \frac{256}{3065}, the reciprocal of \frac{3065}{256}.

$$x=1\times \frac{256}{3065}$$

Multiply 1 and \frac{256}{3065} to get \frac{256}{3065}.

$$x=\frac{256}{3065}$$