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Phantasy [73]
3 years ago
7

What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
4 0
(X-5)2+3(X-5)+9 = 0
let expand the equation
(x)x2-(5)x2 + 3(x)-3(5) + 9 = 0
2x-10+3x-15+9=0
collect like terms
2x+3x-10-15+9 =0
5x-10-6 =0
5x-16=0
5x=0+16
5x=16
divide both side by 5 we have
x=16/5
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3 years ago
The product of two consecutive integers is 5 more than three time the larger. What are the integers?
kvasek [131]
When calculating consecutive integers, the smaller number is x and the larger number is (x + 1).
So the equation you can use is x + (x + 1) = 5 + 3(x + 1)
This is because the sum of the consecutive integers are equal to 5 more than 3 times the larger integer.
Now simplify:
x + (x + 1) = 5 + 3(x + 1)
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2x + 1 = 3x + 8
Now isolate the variable:
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Subtract 2x from both sides:
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Subtract 8 from both side:
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x = -7
So the smaller number is -7 and the larger number is -6.

Now check your answer:
-7 + (-7 + 1) = 5 + 3(-7 + 1)
-7 + (-6) = 5 + 3(-7 + 1)
-7 + (-6) = 5 + 3(-7 + 1)
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-13 = 5 + 3(-6)
-13 = 5 + (-18)
-13 = 5 - 18
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So the integers are -7 and -6.
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Answer:

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3 0
2 years ago
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