4x2-13x+3=0 Two solutions were found :
x = 1/4 = 0.250
x = 3Step by step solution :
Step 1 :Equation at the end of step 1 : (22x2 - 13x) + 3 = 0
Step 2 :Trying to factor by splitting the middle term
2.1 Factoring 4x2-13x+3
The first term is, 4x2 its coefficient is 4 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 4 • 3 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is -13 .
-12 + -1 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -1
4x2 - 12x - 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-3)
Add up the last 2 terms, pulling out common factors :
1 • (x-3)
Step-5 : Add up the four terms of step 4 :
(4x-1) • (x-3)
Which is the desired factorization
Equation at the end of step 2 : (x - 3) • (4x - 1) = 0
Step 3 :Theory - Roots of a product :
3.1 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 :
3.2 Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3
Solving a Single Variable Equation :
3.3 Solve : 4x-1 = 0
Add 1 to both sides of the equation :
4x = 1
Divide both sides of the equation by 4:
x = 1/4 = 0.250
