splitting of х2+x-30=0
Answers
Answer:
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring x2-x-30
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -30
Step-1 : Multiply the coefficient of the first term by the constant 1 • -30 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -1 .
Step-by-step explanation:
-30 + 1 = -29
-15 + 2 = -13
-10 + 3 = -7
-6 + 5 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 5
x2 - 6x + 5x - 30
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
5 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x+5) • (x-6)
Which is the desired factorization
Equation at the end of step
1
:
(x + 5) • (x - 6) = 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+5 = 0
Subtract 5 from both sides of the equation :
x = -5
Solving a Single Variable Equation:
2.3 Solve : x-6 = 0
Add 6 to both sides of the equation :
x = 6
Supplement : Solving Quadratic Equation Directly
Solving x2-x-30 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula