What is the solution set of x2 – 10 = 30x?

So for this, I will be completing the square to solve for x. Firstly, add 10 and subtract 30x on both sides of the equation:

Next, we want to make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and square the quotient. Once you get that result, add it to both sides of the equation:

Now, factor the left side:

Next, square root both sides:

Now, add 15 to both sides of the equation:

This is the exact solution. To find the approximate solution, solve the left side twice -- once with the plus sign, once with the minus sign:

In short: