14. (2x - 1)(x + 7) = 0Using the zero factor property, we know that either the first or second terms (or both) must be equal to 0 if their product is 0. We can set each term equal to 0 to find the solutions:
2x - 1 = 0
2x = 1
x = 1/2
x + 7 = 0
x = -7
15. 
To solve this equation, you first need to set it equal to 0:

Next, it can be factored:

Finally, we can solve just like we did above:
x + 5 = 0
x = -5
x - 2 = 0
x = 2
16. 
First, you can simplify by dividing each side by 4:

Now, set the equation equal to 0:

Next, factor:

Finally, find the solutions:
x + 5 = 0
x = -5
x - 5 = 0
x = 5
Answer:
y=2x-7
Step-by-step explanation:
m==2
y=mx+b
9=16-7
y=2x-7
Answer:
8 1/3 inches
Step-by-step explanation:
Length of the ribbon = 2 1/12 inches
Blue ribbon is 4 time as many inches as long as red
Length of the blue ribbon = 4 * 2 1/12
Length of the blue ribbon = 4 * 25/12
Length of the blue ribbon = 100/12
Length of the blue ribbon= 25/3
Length of the blue ribbon = 8 1/3 inches
Hence the blue ribbon is 8 1/3 inches long
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.