Find the value of T for 5T = 125
Answers
Step-by-step explanation:
3.2 Factoring t2 - 10t + 25
The first term is, t2 its coefficient is 1 .
The middle term is, -10t its coefficient is -10 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 1 • 25 = 25
Step-2 : Find two factors of 25 whose sum equals the coefficient of the middle term, which is -10 .
-25 + -1 = -26
-5 + -5 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -5
t2 - 5t - 5t - 25
Step-4 : Add up the first 2 terms, pulling out like factors :
t • (t-5)
Add up the last 2 terms, pulling out common factors :
5 • (t-5)
Step-5 : Add up the four terms of step 4 :
(t-5) • (t-5)
Which is the desired factorization
Multiplying Exponential Expressions:
3.3 Multiply (t-5) by (t-5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (t-5) and the exponents are :
1 , as (t-5) is the same number as (t-5)1
and 1 , as (t-5) is the same number as (t-5)1
The product is therefore, (t-5)(1+1) = (t-5)2
Equation at the end of step
3
:
-5 • (t - 5)2 = 0
STEP
4
:
Equations which are never true
4.1 Solve : -5 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.2 Solve : (t-5)2 = 0
(t-5) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : t-5 = 0
Add 5 to both sides of the equation :
t = 5
Supplement : Solving Quadratic Equation Directly
Solving t2-10t+25 = 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
Parabola, Finding the Vertex:
5.1 Find the Vertex of y = t2-10t+25