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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