Mathematics, 29.09.2019 14:00 ryliepeloquinf

Which of the following is a solution of 3x2 = 7x - 3? a. negative 7 plus or minus the square root of 13 divided by 6 b. 7 plus or minus the square root of 85 divided by 6 c. negative 7 plus or minus the square root of 85 divided by 6 d. x - 7 plus or minus the square root of 13 divided by 6

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3x^2 = 7x - 3
Rearranging,
3x^2 - 7x + 3 = 0
Using quadratic formula :
x= [7 + sqrt (49 - 36)]/6
x= [7 + sqrt 13]
or
x= [7 - sqrt (49 - 36)]/6
x= [7 - sqrt 13]/6

d. x - 7 plus or minus the square root of 13 divided by 6

Answer from: bentonknalige

The solutions for the equation $3x^{2} =7x-3$ are: $x_{1}=\frac{7+\sqrt{13}}{6} , x_{2}= \frac{7-\sqrt{13} }{6}$ , so the option d is correct.

Step-by-step explanation:

You have two options to find the solutions of the equation $3x^{2} =7x-3$

The first is to solve it with the quadratic formula, for this, you need to follow these steps:

Add 3 and substract 7x from both sides $3x^{2} +3-7x=7x+3-3-7x$ Simplify $3x^{2} +3-7x=0$ Use the quadratic equation formula. For a quadratic equation of the form $ax^{2} +bx+c=0$ the solutions are $x_{1,2} = \frac{-b\±\sqrt{b^{2}-4ac } }{2a}$ In the equation given a=3, b=-7, c=3

, so $x_{1} = \frac{-(-7)+\sqrt{(-7)^{2}-4*3*3 } }{2*3}, x_{2} = \frac{-(-7)-\sqrt{(-7)^{2}-4*3*3 } }{2*3}$ The solutions are $x_{1}=\frac{7+\sqrt{13}}{6} , x_{2}= \frac{7-\sqrt{13} }{6}$

The second option is solve the equation by completing the square:

Substract 7x from both sides $3x^{2} -7x=7x-7x-3$ and simplify $3x^{2} -7x=-3$ Divide both sides by 3 $\frac{3x^{2}-7x }{3}= -\frac{3}{3}$ and simplify $x^{2} -\frac{7x}{3}=-1$ Use the fact that $x^{2} +2ax+a^{2}=(x+a)^{2}$ We need to find

, for this, we use this relation $2ax=-\frac{7x}{3}$ and solve for

, we get $a = -\frac{7}{6}$ Add $a^{2} = (\frac{-7}{6} )^{2} =\frac{13}{36}$ to both sides in the equation of step 2 $x^{2} -\frac{7x}{3}+(-\frac{7}{6} )^{2}=-1 +(-\frac{7}{6} )^{2}$ and simplify $x^{2} -\frac{7x}{3}+(-\frac{7}{6} )^{2}=\frac{13}{36}$ Complete the square, use step 3, $x^{2} -\frac{7x}{3}+(-\frac{7}{6} )^{2} = (x-\frac{7}{6} )^{2}=\frac{13}{36}$ For $f^{2}(x)$ the solutions are $f(x) =\sqrt{a},-\sqrt{a}$ , so $x-\frac{7}{6} = \sqrt{\frac{13}{36} } =\frac{\sqrt{13}+7 }{6}\ and \ x-\frac{7}{6} = -\sqrt{\frac{13}{36} } =-\frac{\sqrt{13}+7 }{6}$

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

ask the math teacher she or he would know lol.

step-by-step explanation:

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