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elena-s [515]
3 years ago
8

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

Mathematics
1 answer:
GaryK [48]3 years ago
8 0

Answer:

  • The two solutions are:           x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

  • The next and every step are below.

Explanation:

1. -3=-2x^2+2x    : Given (addition property / add - 3 to both sides)

2. -3 = - 2(x^2-x)    : Given (commom factor - 2)

3. -3-1/2=-2(x^2-x+1/4)

    To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.

Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.

4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:

-7/2=-2(x-1/2)^2

5. Divide both sides by - 2 to get the next expression:

-7/4=(x-1/2)^2

6. The last step is to extract squere root from both sides of the equality:

(x-1/2)=+/-\sqrt{\frac{7}{4}}\\ \\ x-1/2=+/-\frac{\sqrt{7} }{2}\\ \\ x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

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A number n divided by 12 is 10.<br> - or n =
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A sample of n = 5 scores has a mean of m = 8. one new score is added to the sample and the new mean is calculated to be m = 9. w
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Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x
GuDViN [60]
An even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3


a simple test is the following

if f(x) is even then f(-x)=f(x)
if f(x) is odd then f(-x)=-f(x)


so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
not same because the original has -2x
not even


g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even



g(x)=2x²+1 is the even function
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