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vagabundo [1.1K]
2 years ago
13

2x2 – 5x + 67 = 0 What would be your first step in completing the square for the equation above?

Mathematics
1 answer:
7nadin3 [17]2 years ago
4 0

Answer:

The first step is to divide all the terms by the coefficient of x^{2} which is 2.

The solutions to the quadratic equation 2x^2\:-\:5x\:+\:67\:=\:0 are:

x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}

Step-by-step explanation:

Considering the equation

2x^2\:-\:5x\:+\:67\:=\:0

The first step is to divide all the terms by the coefficient of x^{2} which is 2.

so

\frac{2x^2-5x}{2}=\frac{-67}{2}

x^2-\frac{5x}{2}=-\frac{67}{2}

Lets now solve the equation by completeing the remaining steps

Write equation in the form: x^2+2ax+a^2=\left(x+a\right)^2

Solving for a,

2ax=-\frac{5}{2}x

a=-\frac{5}{4}

\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}

x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{67}{2}+\left(-\frac{5}{4}\right)^2

x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{511}{16}

Completing the square

\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For f^2\left(x\right)=a the solution are f\left(x\right)=\sqrt{a},\:-\sqrt{a}

Solving

x-\frac{5}{4}=\sqrt{-\frac{511}{16}}

x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}

x-\frac{5}{4}=i\sqrt{\frac{511}{16}}       ∵ Applying imaginary number rule \sqrt{-1}=i

x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}

-\frac{5}{4}=i\frac{\sqrt{511}}{4}

x=\frac{5}{4}+i\frac{\sqrt{511}}{4}

Similarly, solving

x-\frac{5}{4}=-\sqrt{-\frac{511}{16}}

x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}    ∵ Applying imaginary number rule  \sqrt{-1}=i

x=\frac{5}{4}-i\frac{\sqrt{511}}{4}

Therefore, the solutions to the quadratic equation are:

x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}

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determine if each polygons are similar, if so, write the similarity statement and the similarity ratio. if not explain why.
Delicious77 [7]

Answer:

They are not similar

Step-by-step Explanation:

For two polygons to be considered similar, two conditions must be met:

1. The ratio of their corresponding sides must be equal, and must have the same scale factor.

2. Their corresponding angles must be the same. That is, the corresponding angles must be congruent.

Now let us examine the two polygons ( ∆AYP and ∆BOX) given to ascertain if they are similar.

First, we can observe that only two of their corresponding sides were given. The third corresponding side, "YP/OX" is not given. This makes it difficult for us to tell if the polygons are similar, if we are to base our conclusion on merely considering the ratio of their corresponding sides.

Although, the two given corresponding sides (AY/BO & AP/BX), both have equal ratio ⅖, i.e. AY/BO = AP/BX = ⅖. This is not enough to tell both polygons are similar, as we cannot tell if the third corresponding side would give us same ratio, since it wasn't given in the diagram.

==>Next is to examine the interior angles of the polygons, whether the measure of their corresponding angles are the same.

Thus, from the diagram, we can see that two angles of the each triangle were given. We can find the measure of the third angle not given since we know that sum of the interior angles of a triangle = 180°

Thus, <P in ∆AYP = 180 - (90+20) = 180 - 110

<P = 70°

Thus, <B in ∆BOX = 180 - (90+80) = 180 - 170

<B = 10°

From the above calculation, comparing both polygons having known the measures of their corresponding angles, we can conclude that both polygons given in the question are not similar.

This is because the measure of their corresponding angles are not congruent.

<A is not congruent to <B, so likewise with <P and <X.

4 0
3 years ago
Pls help me and give all the steps, i am still trying to figure this out
mixer [17]

Answer:

Step-by-step explanation:

Refer to attachment

Wait it is y^10 not y^6 in the answer sorry it was a typo ;(

7 0
3 years ago
In 2012, the total population of Florida was 3,158,697 people. What was the population in scientific notation, approximately?
weeeeeb [17]
That would be 3.158697 * 10^6
5 0
3 years ago
Read 2 more answers
Peter takes an 8-inch by 3-inch sheet of paper and cuts from one corner of the paper to the diagonally opposite corner. now pete
tekilochka [14]
First get the length of the side the was cut (Hypotenuse).

We can use Pythagorean theorem: a^2+b^2 = c^2
a = 8, b = 3 = 1.5, c = ?

plug into forumla

8^2 + 3^2 = 73

a=8,
b=1.5,
c = sqrt( 73) or 8.5

Now add all sides together to get perimeter...
8+3+8.5 = 19.5

The perimeter of each sheet is 19.5in.
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3 years ago
Simplify by using the distributive property and then combining like terms for the expression 7(2x+3)
max2010maxim [7]

Answer:

14x+21

Step-by-step explanation:

7*2x=14x

7*3=21

14x+21

hope this helps :9

6 0
2 years ago
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