Answer: -7twice
Step-by-step explanation:
This is a question on root of quadratic equation. The interpretation of the question
x² 14x + 49 is
x² + 14x + 49 = 0.meaning that we are to find two possible values for x that will make the expression equal 0.
We can use any of the methods earlier taught. For the purpose of this class, I am using factorization methods
x² + 14x + 49 = 0
Now, find the product of the first and the last terms, is
x² × 49 = 49ײ
Now find two terms such that their productbis 49x² and their sum equals 14x, the one in the middle.
We have several factors of 49x² but only one will give sum of 14x. Because of the time, I will only go straight to the required factors .
49x² = 7x × 7x and the sum gives 14x the middle terms..
Now we now replace the middle one by the factors and then factorize by grouping.
x² + 14x + 49 = 0
x² + 7x + 7x + 49 = 0
x(x + 7) + 7(x + 7) = 0
(x + 7)(x + 7). = 0
Now to find this value of x,
x + 7 = 0
x. = -7twice.
The root of the equation = -7twice.
To translate a function up or down you add a constant to the function...2 units downward means you must subtract 2 from the original equation...
g(x)=f(x)-2
g(x)=2x^2-8-2
g(x)=2x^2-10
Answer: x" = 5.69
Step-by-step explanation:
The graphic solution is attached.
Verifying the solution:
Existence condition: x > 0
2x - 4 = √x + 5
√x =2x - 4 - 5
√x =2x - 9 (²)
x = (2x - 9)²
x = 4x² - 36x + 81
4x² - 36x - x + 81 = 0
4x² - 37x + 81 = 0
Δ = -37² - 4.4.81 = 1369 - 1296 = 73
x = 37 ±√73/8
x' = 3.55
x" = 5.69
checking:
2*3.55 - 4 = 3.1
√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution
2*5.69 - 4 = 7.39
√5.69 + 5 = 7.39 ∴ it's the only solution
