y^2-14y-12=0 quadratic formula
Answers
Answer:
Step by Step Solution:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*y^2-14*y-(-12)=0
Step by step solution :
STEP1:Equation at the end of step 1
(2y2 - 14y) - -12 = 0
STEP2:
STEP3:Pulling out like terms
3.1 Pull out like factors :
2y2 - 14y + 12 = 2 • (y2 - 7y + 6)
Trying to factor by splitting the middle term
3.2 Factoring y2 - 7y + 6
The first term is, y2 its coefficient is 1 .
The middle term is, -7y its coefficient is -7 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -7 .
-6 + -1 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -1
y2 - 6y - 1y - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-6)
Add up the last 2 terms, pulling out common factors :
1 • (y-6)
Step-5 : Add up the four terms of step 4 :
(y-1) • (y-6)
Which is the desired factorization
Equation at the end of step3:
2 • (y - 1) • (y - 6) = 0
STEP4:Theory - Roots of a product
4.1 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.
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