Question

What are the solutions to the equation?x² + 3x - 54​

Answer 1

Answer:

x = - 9, x = 6

Step-by-step explanation:

Given

x² + 3x - 54

To find the solutions equate to zero

x² + 3x - 54 = 0 ← in standard form

(x + 9)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 6 = 0 ⇒ x = 6

Answer 2

Answer:

(x+6)⋅(x−9)

Step by Step

Factoring  x2-3x-54  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -3x  its coefficient is  -3 .

The last term, "the constant", is  -54  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -54 = -54  

Step-2 : Find two factors of  -54  whose sum equals the coefficient of the middle term, which is   -3 .

     -54    +    1    =    -53  

     -27    +    2    =    -25  

     -18    +    3    =    -15  

     -9    +    6    =    -3    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  6  

                    x2 - 9x + 6x - 54

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-9)

             Add up the last 2 terms, pulling out common factors :

                   6 • (x-9)

Step-5 : Add up the four terms of step 4 :

                   (x+6)  •  (x-9)

            Which is the desired factorization