Kathy Williams

2021-12-31

Solve the following equation algebraically. Explain your process.

$0=18{x}^{4}+87{x}^{3}+3{x}^{2}-108x$

Hattie Schaeffer

Beginner2022-01-01Added 37 answers

Step 1

Given equation is:

$18{x}^{4}+87{x}^{3}+3{x}^{2}-108x=0$

Taking 3x as common term we get,

$3x(6{x}^{3}+29{x}^{2}+x-36)=0$

So either,

$3x=0$

$x=0$

Or$6{x}^{3}+29{x}^{2}+x-36=0$

Step 2

Splitting up the second and third terms we get,

$6{x}^{3}-6{x}^{2}+35{x}^{2}-35x+36x-36=0$

$6{x}^{2}(x-1)+35x(x-1)+36(x-1)=0$

Taking$(x-1)$ as common term we get,

$(x-1)(6{x}^{2}+35x+36)=0$

Using middle term factorization we get,

$(x-1)(6{x}^{2}+8x+27x+36)=0$

$(x-1)[2x(3x+4)+9(3x+4)]=0$

$(x-1)(3x+4)(2x+9)=0$

$(x-1)=0;(3x+4)=0;(2x+9)=0$

$x=1;x=-\frac{4}{3};x=-\frac{9}{2}$

Hence the roots of the given equation is:

$x=0;x=1;x=-\frac{4}{3};x=-\frac{9}{2}$ .

Given equation is:

Taking 3x as common term we get,

So either,

Or

Step 2

Splitting up the second and third terms we get,

Taking

Using middle term factorization we get,

Hence the roots of the given equation is:

eskalopit

Beginner2022-01-02Added 31 answers

Factor out common term 3x:

Factor

karton

Expert2022-01-04Added 613 answers

We move all terms to the left:

We add all the numbers together, and all the variables

We get rid of parentheses

We add all the numbers together, and all the variables

a=-3; b=3; c=0;

The delta value is higher than zero, so the equation has two solutions.

NSK

We use following formulas to calculate our solutions:

alenahelenash

Expert2023-06-12Added 556 answers

star233

Skilled2023-06-12Added 403 answers

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