Factor the expression over the complex numbers. x^2+52

Here we are given the expression:

Now let us equate it to zero to find x first,

Now subtracting 52 from the other side,

taking square root on both sides,

So we will get two values of x as ,

Now we can write square root -1 as i,

So our factors become,

The final factored form becomes,

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so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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