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Novay_Z [31]
3 years ago
14

Determine the next step for solving the quadratic equation by completing the square.

Mathematics
1 answer:
Studentka2010 [4]3 years ago
4 0

Answer:

The solutions are x=\frac{1+\sqrt{7}}{2} and x=\frac{1-\sqrt{7}}{2}

Step-by-step explanation:

we have

0=-2x^{2}+2x+3

Group terms that contain the same variable, and move the constant to the opposite side of the equation

-3=-2x^{2}+2x

Factor the leading coefficient

-3=-2(x^{2}-x)

Complete the square. Remember to balance the equation by adding the same constants to each side.

-3-0.5=-2(x^{2}-x+0.5^{2})

-3.5=-2(x^{2}-x+0.5^{2})

Rewrite as perfect squares

-3.5=-2(x-0.5)^{2}

7/4=(x-0.5)^{2}

square root both sides

x-0.5=(+/-)\sqrt{\frac{7}{4}}

x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}

x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}

x=\frac{1+\sqrt{7}}{2}

x=\frac{1-\sqrt{7}}{2}

You might be interested in
Suppose that the given line has a slope of -2/3 and a y-intercept of (0,5/3). which of the following points is also a solution t
otez555 [7]

Answer:

From five given points it is find that points (1 , 1) and (4 , -1) will apply

Step-by-step explanation:

According to question,

Slop of line (m) = \frac{-2}{3}

And y-intercept is ( 0, \frac{5}{3})

So from above slope and points, the equation of line can be written as

y = mx + c

i.e \frac{5}{3} = \frac{-2}{3} x + c

    \frac{5}{3} = \frac{-2}{3} (0) + c

    \frac{5}{3} = 0 + c

Or, c = \frac{5}{3}

A) With points ( 5, \frac{5}{3} )

   At x = 5, y =\frac{-2}{3} (5) + \frac{5}{3}

            or, y = \frac{-10}{3} + \frac{5}{3}

            so, y = \frac{-5}{3}

Hence this points do not apply

B) With points ( 1 , 1 )

   At x = 1, y =  \frac{-2}{3} (1) +  \frac{5}{3}

      or,      y =  \frac{-2+5}{3}

      So,     y =  \frac{3}{3}

                y = 1

Hence this points will apply

C) With points ( 4 , -1 )

    At x = 4 , y =  \frac{-2}{3} (4) +  \frac{5}{3}

                    y =  \frac{-8+5}{3}

                    y =  \frac{-3}{3}

             So,  y= -1

Hence this points will apply

D) With points (-3 ,7)

    At x = - 3, y = \frac{-2}{3} (-3) +  \frac{5}{3}

                     y = \frac{14}{3}

 Hence this point will not apply

E) with points (0 , 0)

    At x 0,     y =  \frac{-2}{3} (0) +  \frac{5}{3}

               Or, y = 0 +  \frac{5}{3}

                     y =  \frac{5}{3}

Hence this point will not apply

∴ From above five given points it is find that points (1 , 1) and (4 , -1) apply

Answer

7 0
3 years ago
Multiply 1 5/8 * 2 2/5
ElenaW [278]
39/10
And/or
3 9/10
And/Or
3.9
5 0
4 years ago
Eight hotdogs at the basketball park cost $28 how much does one hotdog cost
Igoryamba
28 divided by 8 is equal to 3.5, so one hotdog will cost $3.50
6 0
3 years ago
Solve by factoring:4x^6+4x^5-24^4=0
Len [333]

Answer:

you could only get to “4x^6+4x^5-331776=0” that would be the simpliest form

Step-by-step explanation:

6 0
3 years ago
An editor is paid $25 an hour to edit 3 essays and an additional $50 bonus when the edits on all three essays are completed. If
Elza [17]

Answer:

B) 25x + 50, where x is the number of hours .

Solution:

Let x be the number of hours editor takes to edit 3 essays.

The editor is paid $25 an hour .

Amount earned in x hours = 25x

Additional bonus given after  edition of three essays = $50.

Total amount earned by the editor = 25x+50

The right option is :

B) 25x + 50, where x is the number of hours






3 0
4 years ago
Read 2 more answers
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