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:<span> Step 1:</span> Trying to factor by splitting the middle term
<span> 1.1 </span> Factoring <span> x2-5x-36</span>
The first term is, <span> <span>x2</span> </span> its coefficient is 1.
The middle term is, <span> -5x </span> its coefficient is - 5.
The last term, "the constant", is <span> -36 </span>
Step-1: Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -36 = -36</span>
Step-2: Find two factors of -36 whose sum equals the coefficient of the middle term, which is - 5.
<span><span> -36 + 1 = -35</span><span> -18 + 2 = -16</span><span> -12 + 3 = -9</span><span> -9 + 4 = -5 That's it</span></span>
Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
<span>x2 - 9x</span> + 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
<span>Equation at the end of step 1 :</span> (x + 4) • (x - 9) = 0 <span>Step 2 :</span>Theory - Roots of a product :
<span> 2.1 </span> A product of several terms equals zero.<span>
</span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span>
</span>We shall now solve each term = 0 separately<span>
</span>In other words, we are going to solve as many equations as there are terms in the product<span>
</span>Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
<span> 2.2 </span> Solve : x+4 = 0<span>
</span>Subtract 4 from both sides of the equation :<span>
</span> x = -4
Solving a Single Variable Equation :
<span> 2.3 </span> Solve : x-9 = 0<span>
</span>Add 9 to both sides of the equation :<span>
</span> x = 9
