factorise
20t square -27t-99
Answers
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Answer:
t=− 4/3
=−0.750
t= 5 \4
=0.800
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
20*t^2-(t+12)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
(22•5t2) - (t + 12) = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 20t2-t-12
The first term is, 20t2 its coefficient is 20 .
The middle term is, -t its coefficient is -1 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 20 • -12 = -240
Step-2 : Find two factors of -240 whose sum equals the coefficient of the middle term, which is -1 .
-240 + 1 = -239
-120 + 2 = -118
-80 + 3 = -77
-60 + 4 = -56
-48 + 5 = -43
-40 + 6 = -34
-30 + 8 = -22
-24 + 10 = -14
-20 + 12 = -8
-16 + 15 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 15
20t2 - 16t + 15t - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
4t • (5t-4)
Add up the last 2 terms, pulling out common factors :
3 • (5t-4)
Step-5 : Add up the four terms of step 4 :
(4t+3) • (5t-4)
Which is the desired factorization
Equation at the end of step
2
:
(5t - 4) • (4t + 3) = 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 : 5t-4 = 0
Add 4 to both sides of the equation :
5t = 4
Divide both sides of the equation by 5:
t = 4/5 = 0.800
Solving a Single Variable Equation:
3.3 Solve : 4t+3 = 0
Subtract 3 from both sides of the equation :
4t = -3
Divide both sides of the equation by 4:
t = -3/4 = -0.750