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sukhopar [10]
3 years ago
10

Solve the following quadratic equation by completing the square ✓3x^2 + 10x + 7✓3 = 0​

Mathematics
1 answer:
solmaris [256]3 years ago
5 0

\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 =   \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 =    -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}

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Which of the following expressions is equal to 3x^2 + 27
Kisachek [45]
Factor: 
3x^2 + 27
= 3(x^2  + 9)
Answer is 3(x^2 + 9), when factored.


A) (3x + 9i)(x + 3i)
= (3x + 9i)(x + 3i)
= (3x)(x) + (3x)(3i) + (9i)(x) + (9i)(3i)
= 3x^2 + 9ix + 9ix + 27i^2
= 27i^2 + 18ix + 3x^2



B) (3x - 9i)(x + 3i)
= (3x +  - 9i)(x + 3i)
= (3x)(x) + (3x)(3i) + ( - 9i)(x) + (- 9i)(3i)
= 3x^2 + 9ix - 9ix - 27i^2
= 27i^2 + 3x^2


C) (3x - 6i)(x + 21i)
= (3x +  - 6i)(x + 21i)
= (3x)(x) + (3x)(21i) + (- 6i)(x) + ( -6i)(21i)
= 3x^2 + 63ix - 6ix - 126i^2
=  - 126i^2 + 57ix + 3x^2






D) (3x - 9i)(x - 3i)
=  (3x +   - 9)(x +  - 3)
= (3x)(x) + (3x)( - 3i) + (- 9)(x) + ( - 9)( - 3i)
= 3x^2 - 9ix - 9x + 27i
= 9ix + 3x^2 + 27i - 9x









Hope that helps!!!

8 0
3 years ago
Read 2 more answers
(-10) - |(-20) – (+30) |
myrzilka [38]

ANSWER: -60

EXPLANATION: To solve for (-10) - |(-20) – (+30) |, we need to do:

−10−| −20 − 30|, which equals −10−|−50|. Next, we do −10−50, which is -60.

−10−|−20−30|

= −10−|−50|

= −10−50

= −60

6 0
2 years ago
How much is three half’s plus one fifth
Maslowich

Let's make it an expression.

Three half's= 3/2 Plus= + one fifth= 1/5

We need to turn 3/2 and 1/5 so that they have the same denominator. Let's use 10.

3/2→15/10 1/5→2/10

15/10+2/10=17/10=1 7/10

So, three half's plus one fifth is 1 7/10.

7 0
3 years ago
Read 2 more answers
Help? I cannot get my head around it.
sergejj [24]

Answer:

60cm³

Step-by-step explanation:

8 0
2 years ago
A 100% increase followed by a 50% decrease
just olya [345]

Answer:

We end up with our original number

Step-by-step explanation:

Let x be our number

We increase by 100

increase = old number * 100%

increase = x*1

increase = x

New number = old number + increase

                       = x+x

                         =2x

Now we decrease by 50%

decrease = number *50%

                = 2x*.5

                =x

Final number = new number - decrease

                       = 2x-x

                         =x

4 0
3 years ago
Read 2 more answers
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