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

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Anis

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

JeffTargetTestPrep

Thank you very much for your simple and time saving approach!

4x^2 - 32x +16=0
For a quadratic equation ax^2 + bx + c = 0, the sum of roots is -b/a

Here, b = -32 and a = 4.
Thus, the sum of roots = -(-32)/4 = 8

Thus, the correct option is E.