Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
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<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
X^2+35=180?
Subtract 35 on each side
x^2=145
Take the square root
x= -sqrt(145)
+sqrt 145...
I hope this helps!!
W + 54 = s
w + 54 = 72
Answer: C
Hope this helps!! :)
Answer:
The square of a prime number is prime
Consider that the initial length and width of the rectangle are given as,
After the length is increased by 10%, the new length (L) of the rectangle is calculated as,
After the width is decreased by 10%, the new width (B) of the rectangle is calculated as,
Then the area (A) of the new rectangle is calculated as,
Thus, the new area of the rectangle is 396 square meters.
