what is the value of x if 893842x^3 is equal to 26478?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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.

Approved by eNotes Editorial
An illustration of the letter 'A' in a speech bubbles

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.

Approved by eNotes Editorial
An illustration of the letter 'A' in a speech bubbles

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.

Approved by eNotes Editorial
An illustration of the letter 'A' in a speech bubbles

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` .

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial