6x^2+28x-5=0 solve by factorization mathod
Answers
Step-by-step explanation:
x=−
6
1
=−0.167
x=
2
5
=2.500
See steps
Step by Step Solution:
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Step by step solution :
STEP
1
:
Equation at the end of step 1
((22•3x2) - 28x) - 5 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 12x2-28x-5
The first term is, 12x2 its coefficient is 12 .
The middle term is, -28x its coefficient is -28 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 12 • -5 = -60
Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -28 .
-60 + 1 = -59
-30 + 2 = -28 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -30 and 2
12x2 - 30x + 2x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
6x • (2x-5)
Add up the last 2 terms, pulling out common factors :
1 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(6x+1) • (2x-5)
Which is the desired factorization
Equation at the end of step
2
:
(2x - 5) • (6x + 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 : 2x-5 = 0
Add 5 to both sides of the equation :
2x = 5
Divide both sides of the equation by 2:
x = 5/2 = 2.500
Solving a Single Variable Equation:
3.3 Solve : 6x+1 = 0
Subtract 1 from both sides of the equation :
6x = -1
Divide both sides of the equation by 6:
x = -1/6 = -0.167
Supplement : Solving Quadratic Equation Directly
Solving 12x2-28x-5 = 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