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What is the sum of all values of that satisfy the equation

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What is the sum of all values of that satisfy the equation  [#permalink]

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New post 01 Nov 2016, 09:45
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What is the sum of all values of that satisfy the equation 4x^2 +16=32x?

A) −8
B) −4√2
C) −4
D) 4√2
E) 8
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Re: What is the sum of all values of that satisfy the equation  [#permalink]

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New post 01 Nov 2016, 10:20
First, lets rearrange the equation....

4x^2 - 32x + 16 = 0
or...
x^2 - 8x + 4 = 0


Using the quadratic formula...

x = (8 ± \sqrt{8^2 - 4*4} )/2

x = 4 ± \sqrt{48}
so the sum of the two possible values of x are...

x1 + x2 = 4+ sqrt... + 4 - sqrt...

x1 + x2 = 8 or E
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Re: What is the sum of all values of that satisfy the equation  [#permalink]

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New post 01 Nov 2016, 11:47
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The only way I know how to solve this is using the formula for the sum of the roots of the equation.

I simplified and got x²-8x+4=0

formula for sume is -b/a=-(-8)/1=8 E
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Re: What is the sum of all values of that satisfy the equation  [#permalink]

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New post 01 Nov 2016, 12:51
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Here is my complete Answer,

Don't hesitate if you have any question.

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Re: What is the sum of all values of that satisfy the equation  [#permalink]

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New post 02 Nov 2016, 10:07
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SW4 wrote:
What is the sum of all values of that satisfy the equation 4x^2 +16=32x?

A) −8
B) −4√2
C) −4
D) 4√2
E) 8


We can start by dividing the equation 4x^2 + 16 = 32x by 4 and we have:

x^2 + 4 = 8x

We can now set the equation to zero and factor out to determine x.

x^2 - 8x + 4 = 0

At this stage we see that we will not be able to “cleanly” solve for x; however we can use some of our knowledge of factoring quadratic equations to determine the sum of the values of x that satisfy our given quadratic.

Let’s highlight this idea with a simpler quadratic.

x^2 - 8x + 12 = 0

(x - 6)(x - 2) = 0

x = 6 or x = 2

Thus, the sum of the values that satisfy the equation is 6 + 2 = 8. Notice that “8” is the opposite of the coefficient of x or the opposite of -8.

Following the same logic, we can safely say that the sum of the values that satisfy the equation x^2 - 8x + 4 = 0, is also 8.

Answer: E
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Re: What is the sum of all values of that satisfy the equation  [#permalink]

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Re: What is the sum of all values of that satisfy the equation   [#permalink] 25 Nov 2018, 09:34
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