Solve the quadratic equation x2 - 12x + 23 =0 by completing the square.
1 answer:
Answer:
Completing the square is always confusing, but if you keep in mind it's just a way to write (A + B )^2 so that the problem is in some easier form it makes a bit better sense. A perfect square has some helpful properties.. anyway..
Step-by-step explanation:
Given: - 12x +23 = 0 ( not a perfect square , tough to work with )
take 1/2 of the second term coefficient 12/2 = 6 and square it
- 12x + (
+23 =
-12x +
+23 =
now there is a perfect square :)
(x - 6)^2 =36-23
(x - 6)^2 = 13
take the square root of both side now
x -6 =
x = +6
sooo what is supposed to happen in these problems is that square root of 13 is supposed to work out to something that is easy to find the root of ... maybe in your answers you left out the square roots? so maybe A is right :/
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Answer:
124.5
Step-by-step explanation:
We need to use two different area formulas to get our final answer.
We need the area formula for the triangle = (h*b) / 2; h = height, b = base.
We also need the area for the circle = . r is radius, we will replace pi with 3.14 per instructions.
To start off, let's do the circle. A = 3.14*r^2. r is given to us, r is 8.
So, just plug this into a calculator:
This would be the area of the circle if it was full, however, we only have half of the circle, so we will divide the area in half to get our final circle area, which is 100.48 ft.
Now, for the triangle. Our height is the radius of the circle, which is 8. And our base is 6 feet. Use the formula to get the area for the triangle.
A = 8*6 / 2 = 24
The area of the triangle is 24 feet. Now, we will combine the triangle area and circle area to get our final answer.
100.48 + 24 = 124.48
Round to the nearest hundredth and you get: 124.5 ft^2