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ollegr [7]
2 years ago
5

Solve the equation 0 = x^2 + 4x − 6 for exact values.

Mathematics
1 answer:
koban [17]2 years ago
6 0

Answer:

x = -2 ± √10

Step-by-step explanation:

x^2 + 4x − 6 = 0

Method I - Solve by completing the square

Add 6 to both sides

x^2 + 4x = 6

use half the x coefficient (4/2 = 2) as the complete the square term.

(x + 2)² = 6 + 2²

(x + 2)² = 10

Take the square root of both sides

x + 2 = ±√10

subtract 2 from both sides

x = -2 ± √10

----------------------

M ethod II - Quadratic equation

x = [ -b ± √(b² - 4ac) ]  /  (2a)

x = [ -4 ± √ (4² - 4(1)(-6)) ] / 2

x = [ -4 ± √ (16 + 24) ] / 2

x = [ -4 ± √40 ] / 2

x = [ -4 ± √(4 * 10) ] / 2

x = [ -4 ± 2√10 ] / 2

x = -2 ± √10

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64x⁶ - 27

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</span>64x⁶ - 27 = 4³(x²)³ -3³ = (4x²)³ -3³.  Now, we can use a formula where a=4x², b=3

(4x²)³ -3³ = (4x² -3)((4x²)² +4x²*3 + 3²) =  (4x² -3)(16x⁴ +12x² + 9) 
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Answer: </span>64x⁶ - 27=  (4x² -3)(16x⁴ +12x² + 9) <span>

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4 0
3 years ago
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Sladkaya [172]
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7 0
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ladessa [460]

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Step-by-step explanation:

picture below

7 0
1 year ago
Solve 2x + 5y = 20; 3x - 10y = 37 by elimination. How do you do this? Thank-you!
mr Goodwill [35]

\left\{\begin{array}{ccc}2x+5y=20&\text{multiply both sides by 2}\\3x-10y=37\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+10y=40\\3x-10y=37\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad7x=77\qquad\text{divide both sides by 7}\\.\qquad\boxed{x=11}\\\\\text{Put the value of x to the first equation:}\\\\2(11)+5y=20\\\\22+5y=20\qquad\text{subtract 22 from both sides}\\\\5y=-2\qquad\text{divide both sides by 5}\\\\\boxed{y=-\dfrac{2}{5}}\\\\Answer:\ \boxed{x=11\ and\ y=-\dfrac{2}{5}}

6 0
3 years ago
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AURORKA [14]

Answer:

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Step-by-step explanation:

total amount paid if offer 1 is accepted:

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she will pay $365.40 in interests

total amount paid if offer 2 is accepted:

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she will pay $363 in interests

Compounding interest refers to interest that earns more interest itself, e.g. in the first offer, the $180 of interests charged for the first year will earn $5.40 in extra interests. While offer 2 only charges $60 in interests during the first year which will in turn earn $3 of interests. The difference between both offers is that interest charges in offer 1 earn more interests than the interest in offer 2 = $5.40 - $3 = $2.40

4 0
3 years ago
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