Algebra question

Question

Please find roots of 

9 x squared minus 155 x minus 500 is equal to zero

Answer 1

Find the roots means to solve for x.

 

9x² - 155x - 500 = 0

 

 

We can use the AC method.  This is similar to factoring by grouping.

 

Find the product of the coefficient of x² and the constant term.

 

(9)(-500) = -4500

 

 

Now find two numbers that multiply to -4500 and add to -155.  This tells us that one number is positive while the other is negative.

 

25 and -180 works.  These numbers add up to -155

 

 

So now we can write the equation as

 

9x² + 25x - 180x - 500 = 0

 

 

Rearrange the terms so that the terms that have common factors are together.

 

9x² - 180x + 25x - 500 = 0

 

9x(x - 20) + 25(x - 20) = 0

 

 

The common factor in the grouping is (x - 20).

 

(x - 20)(9x + 25) = 0

 

 

Now use set the factors equal to zero and solve for x from the two parts.