Question

Let ​ f(x)=x2+5x−36 ​. Enter the x-intercepts of the quadratic function in the boxes.

Answer 1

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     x^2-5*x-(36)=0 

Step by step solution: Step 1: Trying to factor by splitting the middle term

 1.1     Factoring  x2-5x-36 

The first term is,  x2  its coefficient is 1.
The middle term is,  -5x  its coefficient is  - 5.
The last term, "the constant", is  -36 

Step-1: Multiply the coefficient of the first term by the constant   1 • -36 = -36 

Step-2: Find two factors of  -36  whose sum equals the coefficient of the middle term, which is - 5.

     -36   +   1   =   -35     -18   +   2   =   -16     -12   +   3   =   -9     -9   +   4   =   -5   That's it

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4 
                     x2 - 9x + 4x - 36

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 :
                    4 • (x-9)
Step-5: Add up the four terms of step 4 :
                    (x+4)  •  (x-9)
             Which is the desired factorization

Equation at the end of step  1  : (x + 4) • (x - 9) = 0 Step  2  :Theory - Roots of a product :

 2.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 2.2      Solve  :    x+4 = 0 

 Subtract  4  from both sides of the equation : 
                      x = -4 

Solving a Single Variable Equation :

 2.3      Solve  :    x-9 = 0 

 Add  9  to both sides of the equation : 
                      x = 9 

Answer 2

Answer:

$x=-9\text{ or }x=4$

Step-by-step explanation:

We have been given a function and we are asked to find the x-intercept of our given function.

To find the x-intercepts of our given function we will equate our function formula with 0.

$x^2+5x-36=0$  

Now let us factor out our given quadratic equation by splitting the middle term.

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x+9)(x-4)=0$

$(x+9)=0\text{ or }(x-4)=0$

$x+9-9=0-9\text{ or }x-4+4=0+4$

$x=-9\text{ or }x=4$

Therefore, the x-intercepts of our given quadratic functions are $x=-9\text{ or }x=4$.