# 4x^2-16x=48, solve for xIts a math question (but there is oddly not a category for that)

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### 4x^2-16x=48, solve for x

Step 1: turn it into a quadratic equation

4x^2-16x-48 = 0

Step 2: factor the polynomial by factoring out the 4s

**4**(x^2-4x-12) = 0

Now factor the trinomial that you have left

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

If you know how to solve for a solution set, you should be able to work the rest of the problem from there.

You should get a solution set of

(-2,6)

4x^2-16x=48

or, 4(x^2) - 16x - 48 = 0

or, 4[(x^2) - 4x - 12] = 0

or, [(x^2) - 4x - 12] = 0

or, [(x^2) - 6x + 2x - 12] = 0

or, [x(x-6) + 2(x-6)] = 0

or, [(x+2)*(x-6)] = 0

Thus, either, (x+2) = 0 , which gives x = -2 ...........(1)

or, (x-6) = 0 ; which gives x = 6..............(2)

**4x^2-16x=48**

The above can be solved with the help of quadratic formula for that the above equation must be turned into a quadratic equation i.e.

Such that; **4x^2-16x-48=0**

Where, **a=4**

** b=-16**

** c=-48**

We then input the above values into the quadratic formula below, and simplify it, (i have done addition and subtraction separately):

x=[-(-16)+sqrt{(-16)^2-4(4)(-48)}]/2(4)

[-(-16)-sqrt{(-16)^2-4(4)(-48)}]/2(4)

x=[16+sqrt{256+768}]/8

[16-sqrt{256+768}]/8

x=[16+sqrt(1024)]/8

[16-sqrt(1024)]/8

x=[16+32]/8

[16-32]/8

x=48/8

-16/8

**x1=6**

**x2=-2**

**Solution set = (6,-2) Answer.**