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3 years ago

How do you solve x^2-4X-12=0

1 answer:

3 0

x² - 4x - 12 = 0

Factor the left side: (x + 2) · (x - 6) = 0

The equation is true if either factor is zero.

If (x + 2) = 0 then x = -2 .

If (x - 6) = 0 then x = 6 .

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Select the two values of x that are roots of this equation.<br>x + 2x - 6 = 0

VLD [36.1K]

For this case we must solve the following quadratic equation:

$x ^ 2 + 2x-6 = 0$

Where:

$a = 1\\b = 2\\c = -6$

The solution is given by:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

Substituting:

$x = \frac {-2 \pm \sqrt {2 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-2 \pm \sqrt {4 + 24}} {2}\\x = \frac {-2 \pm \sqrt {28}} {2}\\x = \frac {-2 \pm \sqrt {2 ^ 2 * 7}} {2}\\x = \frac {-2 \pm2 \sqrt {7}} {2}\\x = -1 \pm \sqrt {7}$

Thus, we have two roots:

$x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}$

ANswer:

$x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}$

8 0

3 years ago

Use the fundamental identities and appropriate algebraic operations to simplify the following expression. (18 +tan x) (18-tan x)

andrezito [222]

Answer:

a) $\left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)+\sec ^2\left(x\right)=325$

b) The lowest point of $y=\cos \left(x\right)$ , $0\leq x\leq 2\pi$ is when x = $\pi$

Step-by-step explanation:

a) To simplify the expression $\left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)+\sec ^2\left(x\right)$ you must:

Apply Difference of Two Squares Formula: $\left(a+b\right)\left(a-b\right)=a^2-b^2$

$a=18,\:b=\tan \left(x\right)$

$\left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)=18^2-\tan ^2\left(x\right)=324-\tan ^2\left(x\right)$

$324-\tan ^2\left(x\right)+\sec ^2\left(x\right)$

Apply the Pythagorean Identity $1+\tan ^2\left(x\right)=\sec ^2\left(x\right)$

From the Pythagorean Identity, we know that $1=-\tan ^2\left(x\right)+\sec ^2\left(x\right)$

Therefore,

$324[-\tan ^2\left(x\right)+\sec ^2\left(x\right))]\\324[+1]\\325$

b) According with the below graph, the lowest point of $y=\cos \left(x\right)$ , $0\leq x\leq 2\pi$ is when x = $\pi$

3 0

3 years ago

What is 4/2/7 as an improper fraction

Zanzabum

If "4/2/7" is all we have to work with, then PEMDAS rules will save the day. Do the division from left to right.

4/2 becomes 2. Then we have 2/7, a proper fraction. I don't see where an improper fraction would come from in this case.

3 0

3 years ago

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A shoreline is eroding at a rate of 1/3 foot per 3 months . How many feet are eroding per year?

Tatiana [17]

There are 12 months in a yr so 12/3=4 then 1/3x4=4/3 so 1ft and 1/3 erode each yr. C is the correct answer<span />

4 0

2 years ago

ANSWER PLZ QUICK AND FAST WHAT

Marysya12 [62]

the answer is C

Use the distributive property

3 0

2 years ago

Read 2 more answers