Question 349030: (2t-1)(5t-1)=13
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (2t-1)(5t-1)=13
Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
(2t*5t+2t*-1-1*5t-1*-1)=13
Simplify the FOIL expression by multiplying and combining all like terms.
(10t^(2)-7t+1)=13
Remove the parentheses around the expression 10t^(2)-7t+1.
10t^(2)-7t+1=13
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
10t^(2)-7t-12=0
In this problem (4)/(5)*-(3)/(2)=-12 and (4)/(5)-(3)/(2)=-7, so insert (4)/(5) as the right hand term of one factor and -(3)/(2) as the right-hand term of the other factor.
(t+(4)/(5))(t-(3)/(2))=0
Remove the fraction by multiplying the first term of the factor by the denominator of the second term.
(5t+4)(2t-3)=0
Set each of the factors of the left-hand side of the equation equal to 0.
5t+4=0_2t-3=0
Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.
5t+4=0_2t-3=0
Divide each term in the equation by 5.
(5t)/(5)=-(4)/(5)_2t-3=0
Simplify the left-hand side of the equation by canceling the common factors.
t=-(4)/(5)_2t-3=0
Set each of the factors of the left-hand side of the equation equal to 0.
t=-(4)/(5)_2t-3=0
Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
t=-(4)/(5)_2t=3
Divide each term in the equation by 2.
t=-(4)/(5)_(2t)/(2)=(3)/(2)
Simplify the left-hand side of the equation by canceling the common factors.
t=-(4)/(5)_t=(3)/(2)
The complete solution is the set of the individual solutions.
t=-(4)/(5),(3)/(2)
(2t-1)(5t-1)=13
(2t*5t+2t*-1-1*5t-1*-1)=13
(10t^(2)-7t+1)=13
10t^(2)-7t+1=13
In this problem (4)/(5)*-(3)/(2)=-12 and
(4)/(5)-(3)/(2)=-7, so insert (4)/(5) as the right hand term of one factor and
-(3)/(2) as the right-hand term of the other factor.
(t+(4)/(5))(t-(3)/(2))=0
(5t+4)(2t-3)=0
5t+4=0_2t-3=0
(5t)/(5)=-(4)/(5)_2t-3=0
t=-(4)/(5)_2t-3=0
t=-(4)/(5)_2t=3
t=-(4)/(5)_(2t)/(2)=(3)/(2)
t=-(4)/(5)_t=(3)/(2)
t=-4/5,3/2
|
|
|
