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neonofarm [45]
3 years ago
14

Solve for x in the equation x^2+10x+12=36.

Mathematics
1 answer:
Alexandra [31]3 years ago
3 0
Solve for x:
x^2 + 10 x + 12 = 36

36 = 36:
x^2 + 10 x + 12 = 36

Subtract 12 from both sides:
x^2 + 10 x = 24

Add 25 to both sides:
x^2 + 10 x + 25 = 49

Write the left hand side as a square:
(x + 5)^2 = 49

Take the square root of both sides:
x + 5 = 7 or x + 5 = -7

Subtract 5 from both sides:
x = 2 or x + 5 = -7

Subtract 5 from both sides:
Answer:  x = 2 or x = -12 Thus the Answer is A.
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2. Now we want to find the intervals where f'(x) is positive or negative. This is done using critical points, which are the points where f'(x) is either 0 or undefined.

f'(x) =6x^2+6x-180 =0\\\\6x^2+6x-180 = 6\left(x-5\right)\left(x+6\right)=0\\\\x=5,\:x=-6

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Therefore f(x) is increasing \left(-\infty, -6\right) \cup \left(5, \infty\right) and decreasing \left(-6, 5\right)

(b) Now that we know the intervals where f(x) increases or decreases, we can find its extremum points. An extremum point would be a point where f(x) is defined and f'(x) changes signs.

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(c)-(d) An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa).

Concave upward is when the slope increases and concave downward is when the slope decreases.

To find the inflection points of f(x), we need to use the f''(x)

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f(x) is concave down before x = -\frac{1}{2}, concave up after it. So f(x) has an inflection point at x = -\frac{1}{2}.

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