Determine the solution for x2 + 36 > 12x

solution for x^2 + 36 > 12x is x > 6 or x< 6

Step-by-step explanation:

We need to solve the equation:

x^2 + 36 > 12x

Subtract 12x from both sides

x^2 + 36 - 12x > 0

Rearranging

x^2 -12x + 36 > 0

Now factorizing:

x^2 -6x -6x + 36 >0

x(x-6)-6(x-6) > 0

(x-6)(x-6) > 0

(x-6)^2 > 0

For, x^n > 0 and n is even then x >0 or x<0

so,

x-6 >0 or x-6 <0

x > 6 or x< 6

So, solution for x^2 + 36 > 12x is x > 6 or x< 6

For this case we have the following inequality:

We subtract 12x on both sides of the inequality:

We convert to an equation:

To factor the equation, we must find two numbers that when multiplied give +36 and when added together obtain -12. These numbers are -6 and -6.

So, we have:

The solution is

We create test intervals:

We test a value in the interval, such as x = 0:

Is fulfilled!

We test a value in the interval, such as x = 10.

Is fulfilled!

Thus, the solution is given by:

or

or

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step-by-step explanation: