To solve for the value of x in the equation

`893842 x^(3) = 26478`

``divide both sides by 893842

`(893842 x^(3))/(893842) = (26478)/(893842)`

`x^(3) = 0.0296227`

take the cuberoot of both sides

`x = (0.0296227)^(1/3)`

`x = 0.309`

` `

To check your answer, you can substitute the value of x = 0.309 in the original equation.

To find the value of x if

`893842x^3=26478`

we need to isolate x. Divide both sides by 893842

`x^3=26478/893842` now take cube roots

`x=(26478/893842)^{1/3}`

`x approx 0.309`

**The value of x is approximately 0.309.**

Solve `893842x^3=26478` :

Divide both sides by 893842:

`x^3=26478/893842`

Take the cube root of both sides (or raise both sides to the 1/3 power)

**`x=root(3)(26478/893842)~~.3094` Using a calculator you can approximate the answer to the number of digits required.**

Alternatively, you can use a graphing calculator to graph `y=893842x^3-26478` and use the zero function to find the root.

You need to solve for x the following equation, such that:

`893842x^3 = 26478 => 446921x^3 = 13239`

You need to divide by `446921` both sides such that:

`x^3 = 13239/446921 => x^3- 13239/446921 = 0`

You need to use the following formula, such that:

`a^3 - b^3 = (a - b)(a^2 + ab + b^2)`

Reasoning by analogy yields:

`x^3 - 13239/446921 = (x - root(3)(13239/446921))(x^2 + root(3)(x(13239/446921)) + root(3)((13239/446921)^2))`

Since `x^3 - 13239/446921 = 0` , then, you need to solve the following equations, such that:

`{(x - root(3)(13239/446921) = 0),(x^2 + x*root(3)((13239/446921)) + root(3)((13239/446921)^2) = 0):}` `=> {(x_1 = 0.307),(x_(2,3) = (-root(3)(13239/446921) +- sqrt(root(3)(13239/446921)^2 - 4root(3)(13239/446921)^2))/2):}`

**Notice that `x_(2,3) !in R` , hence, the only real solution to the given equation is `x = 0.307` .**